System and method for multi-factor modeling, analysis and margining of credit default swaps for risk offset

ABSTRACT

A system and method for determining a margin requirement associated with a plurality of financial instruments within a portfolio is disclosed. The system and method include receiving a plurality of data associated with the plurality of financial instruments within the portfolio, determining a systematic risk margin based on at least a portion of the received plurality of data, determining a curve risk margin based on at least a second portion of the received plurality of data, determining a convergence and divergence risk margin based on at least a third portion of the received plurality of data, determining a sector risk margin based on at least a fourth portion of the received plurality of data, determining an idiosyncratic risk margin based on at least a fifth portion of the received plurality of data, determining a liquidity risk margin based on at least a sixth portion of the received plurality of data, determining a basis risk margin based on at least a seventh portion of the received plurality of data, and calculating a multi-factor risk margin based on one more of the determined risk factors.

REFERENCE TO RELATED APPLICATIONS

This patent is a continuation-in-part of the following co-pending andcommonly assigned U.S. patent applications, the contents of which arehereby incorporated by reference for all purposes. The priority parentapplications are as follows:

U.S. patent application Ser. No. 12/540,765 titled “SYSTEM AND METHODFOR USING DIVERSIFICATION SPREADING FOR RISK OFFSET”, filed Aug. 13,2009;

U.S. patent application Ser. No. 11/030,815, titled “SYSTEM AND METHODFOR ACTIVITY BASED MARGINING”, filed Jan. 7, 2005;

U.S. patent application Ser. No. 11/030,796, titled “SYSTEM AND METHODFOR EFFICIENTLY USING COLLATERAL FOR RISK OFFSET”, filed Jan. 7, 2005;

U.S. patent application Ser. No. 11/030,833, titled “SYSTEM AND METHODFOR ASYMMETRIC OFFSETS IN A RISK MANAGEMENT SYSTEM”, filed Jan. 7, 2005;

U.S. patent application Ser. No. 11/030,814, titled “SYSTEM AND METHODFOR DISPLAYING A COMBINED TRADING AND RISK MANAGEMENT GUI DISPLAY”,filed Jan. 7, 2005;

U.S. patent application Ser. No. 11/031,182, titled “SYSTEM AND METHODFOR FLEXIBLE SPREAD PARTICIPATION”, filed Jan. 7, 2005;

U.S. patent application Ser. No. 11/030,869, titled “SYSTEM AND METHODFOR HYBRID SPREADING FOR RISK MANAGEMENT”, filed Jan. 7, 2005;

U.S. patent application Ser. No. 11/030,849, titled “SYSTEM AND METHODOF MARGINING FIXED PAYOFF PRODUCTS”, filed Jan. 7, 2005; and

U.S. patent application Ser. No. 11/504,379, (now U.S. Pat. No.7,593,879), titled “SYSTEM AND METHOD FOR USING DIVERSIFICATIONSPREADING FOR RISK OFFSET”, filed Aug. 15, 2006; and

U.S. patent application Ser. No. 11/845,198, titled “ASYMMETRIC ANDVOLATILITY MARGINING FOR RISK OFFSET”, filed Aug. 27, 2007.

COPYRIGHT NOTICE

A portion of the disclosure of this patent document contains materialthat is subject to copyright protection. The copyright owner has noobjection to the facsimile reproduction by anyone of the patent documentor the patent disclosure, as it appears in the Patent and TrademarkOffice patent file or records, but otherwise reserves all copyrightrights whatsoever.

BACKGROUND

Futures Exchanges, referred to herein also as an “Exchange”, such as theChicago Mercantile Exchange Inc. (CME) and the New York MercantileExchange, Inc. (NYMEX), collectively referred to as CME Group, Inc. (CMEGroup), provide a marketplace where futures and options on futures aretraded. The term “futures” designates all contracts covering thepurchase and sale of financial instruments or physical commodities forfuture delivery on a futures exchange or exchange. A futures contract isa legally binding agreement to buy or sell a commodity at a specifiedprice at a predetermined future time. Each futures contract isstandardized and specifies commodity, quality, quantity, delivery dateand settlement. An option is the right, but not the obligation, to sellor buy the underlying instrument (in this case, a futures contract) at aspecified price within a specified time. In particular, a put option isan option granting the right, but not the obligation, to sell a futurescontract at the stated price prior to the expiration date. In contrast,a call option is an option contract which gives the buyer the right, butnot the obligation, to purchase a specific futures contract at a fixedprice (strike price) within a specified period of time as designated bythe Exchange in its contract specifications. The buyer has the right tobuy the commodity (underlying futures contract) or enter a longposition, i.e. a position in which the trader has bought a futurescontract that does not offset a previously established short position. Acall writer (seller) has the obligation to sell the commodity (or entera short position, i.e. the opposite of a long position) at a fixed price(strike price) during a certain fixed time when assigned to do so by aclearing house discussed below. The term “short” refers to one who hassold a futures contract to establish a market position and who has notyet closed out this position through an offsetting procedure, i.e. theopposite of long. Generally, an offset refers to taking a second futuresor options on futures position opposite to the initial or openingposition, e.g. selling if one has bought, or buying if one has sold.

Typically, the Exchange provides a “clearing house” which is a divisionof the Exchange through which all trades made must be confirmed, matchedand settled each day until offset or delivered. The clearing house is anadjunct to the Exchange responsible for settling trading accounts,clearing trades, collecting and maintaining performance bond funds,regulating delivery and reporting trading data. Clearing is theprocedure through which the clearing house becomes buyer to each sellerof a futures contract, and seller to each buyer, and assumesresponsibility for protecting buyers and sellers from financial loss byassuring performance on each contract. This is affected through theclearing process, whereby transactions are matched. A clearing member isa firm qualified to clear trades through the clearing house. In the caseof the CME's clearing house, all clearing members not specificallydesignated as Class B members are considered Class A clearing members.In the CME there are three categories of clearing members: 1) CMEclearing members, qualified to clear transactions for all commodities;2) IMM clearing members, qualified to clear trades for only IMM and IOMcommodities; and 3) IMM Class B clearing members, solely limited toconducting proprietary arbitrage in foreign currencies between a singleExchange-approved bank and the IMM and who must be guaranteed by one ormore Class A non-bank CME or IMM clearing member(s). Note that a“member” is a broker/trader registered with the Exchange.

While the disclosed embodiments will be described in reference to theCME, it will be appreciated that these embodiments are applicable to anyExchange, including those that trade in equities and other securities.The CME clearing house clears, settles and guarantees all matchedtransactions in CME contracts occurring through its facilities. Inaddition, the CME clearing house establishes and monitors financialrequirements for clearing members and conveys certain clearingprivileges in conjunction with the relevant exchange markets.

The clearing house establishes clearing level performance bonds ormargins for all CME products and establishes minimum performance bondrequirements for customers of CME products. A performance bond or marginis the funds that must be deposited by a customer with his or herbroker, by a broker with a clearing member or by a clearing member withthe clearing house, for the purpose of insuring the broker or clearinghouse against loss on open futures or options contracts. This is not apart payment on a purchase. The performance bond helps to ensure thefinancial integrity of brokers, clearing members and the Exchange as awhole. The performance bond to clearing house refers to the minimumdollar deposit which is required by the clearing house from clearingmembers in accordance with their positions. Maintenance, or maintenancemargin, refers to a sum, usually smaller than the initial performancebond, which must remain on deposit in the customer's account for anyposition at all times. The initial margin is the total amount of marginper contract required by the broker when a futures position is opened. Adrop in funds below this level requires a deposit back to the initialmargin levels, i.e. a performance bond call. If a customer's equity inany futures position drops to or under the maintenance level because ofadverse price action, the broker must issue a performance bond/margincall to restore the customer's equity. A performance bond call, alsoreferred to as a margin call, is a demand for additional funds to bringthe customer's account back up to the initial performance bond levelwhenever adverse price movements cause the account to go below themaintenance.

The accounts of individual members, clearing firms and non-membercustomers doing business through CME must be carried and guaranteed tothe clearing house by a clearing member. As mentioned above, in everymatched transaction executed through the Exchange's facilities, theclearing house is substituted as the buyer to the seller and the sellerto the buyer, with a clearing member assuming the opposite side of eachtransaction. The clearing house is an operating division of theExchange, and all rights, obligations and/or liabilities of the clearinghouse are rights, obligations and/or liabilities of CME. Clearingmembers assume full financial and performance responsibility for alltransactions executed through them and all positions they carry. Theclearing house, dealing exclusively with clearing members, holds eachclearing member accountable for every position it carries regardless ofwhether the position is being carried for the account of an individualmember, for the account of a non-member customer, or for the clearingmember's own account. Conversely, as the contra-side to every position,the clearing house is held accountable to the clearing members for thenet settlement from all transactions on which it has been substituted asprovided in the rules.

The clearing house does not look to non-member customers for performanceor attempt to evaluate their creditworthiness or market qualifications.The clearing house does monitor clearing members for the adequacy ofcredit monitoring and risk management of their customers. In addition,although the Exchange has established character and financial standardsfor its individual members, the clearing house looks solely to theclearing member carrying and guaranteeing the account to secure allpayments and performance bond obligations. Further, when an individualmember executes orders for a clearing member, his or herguarantor-clearing member is held accountable as principal for thebrokered transaction until the transaction has been matched and recordedby the clearing house as a transaction of the clearing member for whomthe individual member had acted.

The risk management and financial surveillance techniques employed byCME are designed to:

-   -   Prevent the accumulation of losses;    -   Ensure that sufficient resources are available to cover future        obligations;    -   Result in the prompt detection of financial and operational        weaknesses;    -   Allow swift and appropriate action to be taken to rectify any        financial problems and protect the clearing system.        These techniques are consistent with risk management        recommendations by authoritative organizations.

CME derives its financial stability in large part by removing debtobligations among market participants as they occur. This isaccomplished by determining a settlement price at the close of themarket each day for each contract and marking all open positions to thatprice, referred to as “mark to market.” Every contract is debited orcredited based on that trading session's gains or losses. As prices movefor or against a position, funds flow into and out of the tradingaccount. Debt obligations from option contracts are also immediatelyremoved, since the purchaser of an option must pay the premium (cost ofthe option) in full at the time of purchase. Sellers of options postperformance bonds, discussed above, as determined by the CME accordingto the prevailing risk characteristics of the options sold. In the caseof the CME, each business day by 6:40 a.m. Chicago time, based on themark-to-the-market of all open positions to the previous trading day'ssettlement price, the clearing house pays to or collects cash from eachclearing member. This cash flow, known as settlement variation, isperformed by CME's settlement banks based on instructions issued by theclearing house. All payments to and collections from clearing membersare made in “same-day” funds. In addition to the 6:40 a.m. settlement, adaily intra-day mark-to-the market of all open positions, includingtrades executed during the overnight GLOBEX®, the CME's electronictrading systems, trading session and the current day's trades matchedbefore 11:15 a.m., is performed using current prices. The resulting cashpayments are made intra-day for same day value. In times of extremeprice volatility, the clearing house has the authority to performadditional intra-day mark-to-the-market calculations on open positionsand to call for immediate payment of settlement variation. Settlementvariation payments through the clearing house average $1.4 billion perday and have reached a peak of $6.4 billion. CME's mark-to-the-marketsettlement system stands in direct contrast to the settlement systemsimplemented by many other financial markets, including the interbank,Treasury securities, over-the-counter foreign exchange and debt,options, and equities markets, where participants regularly assumecredit exposure to each other. In those markets, the failure of oneparticipant can have a ripple effect on the solvency of the otherparticipants. Conversely, CME's mark-to-the-market system does not allowlosses to accumulate over time or allow a market participant theopportunity to defer losses associated with market positions.

If a clearing member does not have sufficient performance bondcollateral on deposit with the clearing house, then the clearing membermust meet a call for cash performance bond deposits by 6:40 a.m. and/orby 2:00 p.m. Chicago time, which results in a direct debit to theclearing member's account at one of CME's settlement banks. Clearingmembers' performance bond deposits may only be:

-   -   Cash (such as U.S. dollars, Japanese yen, Euro currency, Swiss        francs, British pounds, Canadian dollars, Australian dollars,        Norwegian krone, and Swedish krona);    -   U.S. Treasury securities;    -   Letters of credit issued in the Exchange's name by approved        banks;    -   Stocks selected from among approximately half of those in the        Standard & Poor's 500® Stock Price Index and depository trust        shares based on the Standard & Poor's 500 Stock Price Index;    -   Selected sovereign debt of Canada, France, Germany, and the UK;    -   Discount notes issued by the Federal Farm Credit Banks, Federal        Home Loan Mortgage Corporation, Federal Home Loan Bank System,        or Fannie Mae, provided that the notes have less than six months        remaining to maturity;    -   Fixed rate note and bond securities issued by the Federal Farm

Credit Bank, Federal Home Loan Bank, Federal Home Loan MortgageCorporation, Fannie Mae or Ginnie Mae;

-   -   Interest Earning Facility (IEFO), a CME managed fund program;    -   IEF2: Money Market Mutual Funds allowable under CFTC Regulation        1.25; and    -   IEF3 and IEF4: Clearing firm self-directed collateral management        program, which allows collateral instruments allowable permitted        under CFTC Regulation 1.25.

Securities are revalued every day and are subject to prudent haircuts.Additionally, foreign cash is subject to haircuts in selectedcircumstances. Various forms of collateral are also subject to limits.

CME's clearing house also maintains a Concentration Margining Program,which allows the clearing house to charge additional performance bondrequirements when clearing firms' potential market exposures becomelarge relative to the financial resources available to support thoseexposures.

In recognition of the growing linkages among the markets forexchange-traded equity derivative products, as well as the need topromote efficient clearing procedures and to focus on the trueintermarket risk exposure of clearing members, CME, in conjunction withthe Options Clearing Corporation (OCC) and the New York ClearingCorporation (NYCC), has developed a cross-margining system with respectto market professionals and proprietary accounts. By combining thepositions of joint or affiliated clearing members in certain broad-basedequity index futures and options into a single portfolio, and utilizingthe sophisticated risk-based systems of each clearing organization, asingle performance bond requirement across both markets is determined.The clearing organizations jointly hold a first lien on and securityinterest in the positions in cross-margined accounts. All performancebond deposits associated with these accounts are jointly held. Thecross-margining system significantly enhances both the efficiency andfinancial integrity of the clearing system by treating all positions asbeing held in the same account, which allows gains accruing to futuresor options positions to be immediately available to meet therequirements for funds from losing positions. In the event that aclearing organization suspends a cross-margining member, the positionsin the cross-margin accounts would be liquidated and all performancebond collateral would be converted to cash and applied toward eachclearing organization's costs of liquidating the cross-margin accounts.CME, the OCC and the NYCC are each entitled to proportional shares ofany surplus to apply toward other obligations of the clearing member; ifone clearing organization did not need its entire share of the surplus,the excess would be made available to the other clearing organizations.

CME also maintains cross-margin agreements with the London ClearingHouse and Fixed Income Clearing Corporation. These programs involve thecross-margining of selected interest rate products. The design of thesetwo cross-margin programs differ from the above mentioned OCC/NYCCprogram in that performance bond collateral is held separately at eachrespective clearing organization. In the event that a clearingorganization suspends a CME/LCH cross-margining participant, thecross-margined positions would be liquidated and performance bondcollateral would be converted to cash at each respective clearingorganization. If as a result of the liquidation of cross-marginedpositions and performance bond there is a resulting cross-margin loss,there will be a cross-margin guarantee payment from one clearingorganization to the other to share the loss. A similarly structuredcross-margin program is in place between CME and NYMEX for NYMEX energyproducts versus CME's commodity index complex.

The Clearing House Division monitors intra-day price movementsthroughout the trading session. To assess the impact of these pricechanges on clearing members, an intra-day mark-to-the-market calculationis performed on clearing member futures and options positions andreviewed by the Clearing House and Risk Management Departments severaltimes each day, more frequently if price volatility is high. Large orconcentrated positions on the losing side of the market receive specialattention. The Audit Department may either contact or visit a clearingfirm to determine whether proper performance bonds have been collectedfor these positions and to determine their impact on the clearingmember's capital position and liquidity.

CME also conducts stress testing of clearing member positions on a dailybasis. Numerous stress scenarios have been modeled to reflect a diverseuniverse of possible market events. Stress results are evaluated againstperformance bond on deposit and also with clearing member adjusted netcapital. Results of stress tests may lead the clearing house to requestthat the clearing member provide additional information about itscustomer accounts such as whether there are non-CME offsetting positionsin other markets. In some cases stress test results may cause theclearing house to increase a clearing member's performance bondrequirement, or reduce or transfer positions.

Through the Division of Market Regulation at CME and working inconjunction with CBOT's Office of Investigations and Audits (OIA), CME'sRisk Management Team has daily access to specific account positioninformation regarding individual members, nonmember customers andclearing members, all of which is maintained on a highly confidentialbasis. Such critical information allows for the identification ofconcentrated positions as they arise and the aggregation of positionsthat may be owned by common principals through several differentclearing members. Knowledge of concentrated or high-risk positions,coupled with information routinely gathered on the cash and/or relatedderivative markets, enables CME to respond rapidly to market situationsthat might adversely affect the clearing system and/or the financialstability of a clearing member.

The Exchanges periodically visit their clearing member firms to reviewtheir financial, operational and risk management procedures andcapabilities. Senior Clearing House staff evaluates how well each firm'sprocedures and capabilities correspond to its line of business. Seniorstaff from Audit, Clearing House, Risk Management, and Market Regulationfollow-up with the clearing member's senior management if there aredeficiencies found in their risk management procedures and capabilities.

Risk management and financial surveillance are the two primary functionsof CME's financial safeguard system. The system is designed to providethe highest level of safety and the early detection of unsound financialpractices on the part of any clearing member. Its purpose is to protectall clearing members and their customers from the consequences of adefault by a participant in the clearing process. The system isconstantly being updated to reflect the most advanced risk managementand financial surveillance techniques.

In order to minimize risk to the Exchange while minimizing the burden onmembers, it is desirable to approximate the requisite performance bondor margin requirement as closely as possible to the actual positions ofthe account at any given time. Accordingly, there is a need to improvethe accuracy and flexibility of the mechanisms that estimate performancebond requirements.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 depicts an exemplary risk management system according to oneembodiment.

FIG. 2 depicts a block diagram of a multi-factor spread-based riskmanagement engine for use with the system of FIG. 1.

FIGS. 3A and 3B depict exemplary performance bond requirements.

DETAILED DESCRIPTION

CME establishes minimum initial and maintenance performance bond levelsfor all products traded through its facilities. CME bases theserequirements on historical price volatilities, current and anticipatedmarket conditions, and other relevant information. Performance bondlevels vary by product and are adjusted to reflect changes in pricevolatility and other factors. Both initial and maintenance performancebonds are good faith deposits to guarantee performance on futures andoptions contracts. Maintenance performance bond levels represent theminimum amount of protection against potential losses at which theExchange will allow a clearing member to carry a position or portfolio.Should performance bonds on deposit at the customer level fall below themaintenance level, Exchange rules require that the account bere-margined at the required higher initial performance bond level.Clearing members may impose more stringent performance bond requirementsthan the minimums set by the Exchanges. At the clearing house level,clearing members must post at least the maintenance performance bondsfor all positions carried. This requirement applies to positions ofindividual members, nonmember customers and the clearing member itself.

In setting performance bond levels, the clearing house monitors currentand historical price movements covering short-, intermediate- andlonger-term data using statistical and parametric and non-parametricanalysis. The clearing house and CME Board of Directors then typicallyset futures maintenance performance bond levels to cover at least themaximum one-day price move on 95% of the days during these time periods.The actual performance bond requirements often exceed this level.Performance bond requirements for options reflect movements in theunderlying futures price, volatility, time to expiration and other riskfactors, and adjust automatically each day to reflect the unique andchanging risk characteristics of each option series. In addition, longoptions must be paid for in full, and CME mandates stringent minimumperformance bonds for short option positions. Exemplar performance bondrequirements are shown in FIGS. 3A and 3B.

CME calculates performance bonds using a system developed andimplemented by CME called Standard Portfolio Analysis of Risk™ (SPAN®).SPAN bases performance bond requirements on the overall risk of theportfolios using parameters as determined by CME's Board of Directors,and thus represents a significant improvement over other performancebond systems, most notably those that are “strategy-based” or“delta-based.” Delta is the measure of the price-change relationshipbetween an option and the underlying futures price and is equal to thechange in premium divided by the change in futures price. SPAN simulatesthe effects of changing market conditions and uses standard optionspricing models to determine a portfolio's overall risk. It treatsfutures and options uniformly while recognizing the unique features ofoptions. In standard options pricing models, three factors most stronglyaffect options values: the underlying futures price, volatility(variability of futures price) and time to expiration. As these factorschange, futures and options may gain or lose value. SPAN constructsscenarios of futures prices and volatility changes to simulate what theentire portfolio might reasonably lose over a one-day time horizon. Theresulting SPAN performance bond requirement covers this potential loss.

SPAN evaluates overall portfolio risk by calculating the worst probableloss that a portfolio might reasonably incur over a specified timeperiod. SPAN achieves this number by comparing hypothetical gains andlosses that a portfolio would sustain under different market conditions.SPAN typically provides a ‘Risk Array” analysis of 16 possible scenariosfor a specific portfolio under various conditions. SPAN methodology,however, allows users to request any number of scenarios to meet theirparticular needs:

-   -   Each scenario consists of a “what-if” situation in which SPAN        assesses the effects 0of variations in price, volatility and        time to expiration; and    -   Each calculation represents a gain or loss based on the possible        gains or losses due to changes in an instrument's price by X and        volatility by Y.

SPAN licensed clearing organizations and exchanges determine forthemselves the following SPAN parameters, in order to reflect the riskcoverage desired in any particular market:

-   -   Price Scan Range: A set range of potential price changes;    -   Volatility Scan Range: A set range of potential implied        volatility changes;    -   Intra commodity Spread Charge: An amount that accounts for risk        (basis risk) of calendar spreads or different expirations of the        same product, which are not perfectly correlated;    -   Short Option Minimum: Minimum margin requirement for short        option positions;    -   Spot Charge: A charge that covers the increased risk of        positions in deliverable instruments near expiration; and    -   Intercommodity Spread Credit: Margin credit for offsetting        positions between correlated products.

SPAN combines financial instruments within the same underlying basis foranalysis, and refers to this grouping as the Combined Commodity group.For example, futures, options on futures and options on equities on thesame stock could all be grouped under a single Combined Commodity.

To calculate a performance bond requirement, for each Combined Commodityin a portfolio, SPAN will:

-   -   Sum the Scan Risk charges, any Intracommodity Spread and Spot        Charges;    -   Apply the offsets for all Intercommodity Spread Credits within        the portfolio;    -   Compare the above sum with any existing Short Option Minimum        requirement; and    -   Assess the greater of the two compared as the risk of the        Combined Commodity.

The Total Margin Requirement for a portfolio is the sum of the risk ofall Combined Commodities less all credit for risk offsets between thedifferent Combined Commodities.

Here's an example of a portfolio with CME Euro FX Futures and Optionspositions:

-   -   Euro FX Futures: I Long June 04    -   Euro FX Options on Futures: 1 Short June/JuneO4 Call1.150 Strike    -   Euro FX June Futures Settlements 1.1960    -   Euro FX Futures Price Scan Range=$2400=192 points    -   Euro FX Volatility Scan Range=1%

One Short June One Long on June O4 June O4 1.150 Call Euro Scenario #Euro FX FX Option Portfolio Description 1 $0 −$130 −$130 Priceunchanged; Volatility up the Scan Range. 2 $0 $155 $155 Price unchanged;Volatility down the Scan Range 3 $800 −$785 $15 Price up ⅓ the PriceScan Range; Volatility vp the Scan Range 4 $800 −$531 $268 Price up 113the Price Scan Range; Volatility down the Scan Range 5 $800 $500 $300Price down 113 the Price Scan Range; Volatility up the Scan Range 6−$800 $815 $15 Price down the ⅓ the Price Scan Range; Volatility downthe Scan Range 7 $1600 −$1463 $137 Price up ⅔ the Price Scan Range;Volatility up the Scan Range 8 $1600 −$1240 $360 Price up ⅔ the PriceScan Range; Volatility down the Scan Range 9 −$1600 $1102 −$498 Pricedown ⅔ the Price Scan Range; Volatility up the Scan Range 10 −$1600$1446 −$154 Price down ⅔ the Price Scan Range; Volatility down the ScanRange 11 $2400 −$2160 $240 Price up 3/3 the Price Scan Range; Volatilitydown the Scan Range 12 $2400 $1967 $433 Price down 3/3 the Price ScanRange; Volatility down the Scan Range 13 −$2400 $1674 −$726 Price downthe Price Scan Range; Vola6lity up the Scan Range 14 −$2400 $2043 −$357Price down 3/3 the Price Scan Range; Volatility down the Scan Range 15$2304 −$2112 $192 Price up extreme (3 times the Price Scan Range) -Cover 32% of loon 16 −$2304 $1466 −$838 Price down extreme (3 times thePrice Scan Range) - Cover 32% of loss

In the sample portfolio above, in scenario 8, the gain on one long June04 EC futures position offsets the loss of one short EC June/June 041.150 call option position, incurring a gain of $360. In scenario 16,the portfolio would incur a loss of $838 over the next trading day,which is 32% of the resulting loss if the price of the underlying futuredecreases by three times the price scan range. After SPAN has scannedthe different scenarios of underlying market price and volatilitychanges, it selects the largest loss among these observations. This“largest reasonable loss” is the Scan Risk charge. In this example, thelargest loss across all 16 scenarios is a result of Scenario 16, a lossof $838.

A number of common features are integrated into the SPAN softwarefamily. All SPAN software products:

-   -   Are Windows-based and have the familiar look and feel of today's        most widely used desktop software products;    -   Feature free access to daily SPAN arrays from a variety of        exchanges and clearing organizations around the world;    -   Feature extensive, detailed and well documented reports on        Portfolio and Risk parameters;    -   Include an XML-based reporting module that provides for simple        data import and export to Access or Excel;    -   Are supported by the CME Clearing House's Risk Management        experts via a dedicated SPAN hot/me and email address;    -   Run in batch or GUI interactive mode and can be automated with        simple scripting language; and    -   Support multiple currencies and the widest possible variety of        instruments including stocks, bonds, OTC derivatives, cash,        futures, and options.

PC-SPAN is single-user desktop software that enables a user to enterpositions manually or by using scripting language to automate theposition entry process. With a click of the mouse, the SPAN requirementis known. As thousands of users can attest, PC-SPAN allows for anextremely quick, inexpensive and simple way to calculate marginrequirements across multiple exchanges.

The SPAN Risk Manager is a single-user, desktop software that integratesrisk management features with the latest processing technology todeliver an extremely flexible, intuitive system for full portfolio riskmanagement. SPAN Risk Manager's powerful features and intuitive designallow for true portfolio analytics through multi-variant stress testingand option exposures.

Specifically, SPAN Risk Manager:

-   -   Enables users to gauge the effects, on a total portfolio or an        individual option, of:    -   Changes in price    -   Implied volatility    -   Time to expiration    -   Dividend yields    -   Interest rates    -   Calculates hypothetical P&L's, option prices, and Greeks    -   Calculates implied, average call/put and series volatilities    -   Allows for stress testing of multiple products    -   Allows user to define, compare, save and reload “What-If”        Scenarios for stress testing    -   Enables the user to shift volatility skews    -   Provides simultaneous analyses on several different trading        instruments    -   Supports the following option pricing models:    -   Black-Scholes    -   Merton    -   Adesi-Whaley    -   Cox-Ross-Rubenstein

At the top of the SPAN software hierarchy is SPAN Risk Manager Clearing.This program employs all of the functionalities of PC-SPAN and SPAN RiskManager plus several additional features that are applicable to entitiessuch as exchanges, clearing organizations, and service bureaus. Thesefeatures include:

-   -   “What-If” Margining—Allows an organization to view and compare        hypothetical margins under multi-variant “What-if” scenarios;    -   Real-Time Component Interface—Allows for real-time SPAN        margining and pro or post execution credit controls;    -   Automated Production and Publication of SPAN Risk Array files        takes the work out of creating a publishing a daily SPAN Risk        Array file to the world; and    -   Complex Implied Volatility Averaging.

As described above, SPAN is utilized by both the Exchange and is alsoprovided as a tool which may be used by clearing members or otherentities to determine their anticipated performance bond requirements.In this way, clearing members, or other entities, may anticipate theperformance bond requirements of the clearing house which facilitatesfinancial planning and certainty. SPAN is also made available as aproduct to be used by clearing houses of other exchanges. It will beappreciated that the disclosed embodiments are equally applicable toboth the version of SPAN used by the exchange and the version used bythe market participants and that any discussion herein referring to SPANis intended to be applicable to both applications.

Another system for assessing risk in a portfolio is the TheoreticalIntermarket Margin System (“TIMS”) manufactured by The Options ClearingCorporation, located in Chicago, Ill. TIMS allows clearing institutionsto measure, monitor and manage the level of risk exposure of theirmembers' portfolios. TIMS can calculate risk exposure at differentaccount levels and for different account types. In addition, TIMS usesportfolio theory to margin all positions relating to the same underlyingproduct and combines the risk of closely related products intointegrated portfolios. This portfolio aspect of TIMS allows for therecognition of hedges used by market participants in increasinglyinterrelated markets. The TIMS methodology allows for measuring themonetary risk inherent in portfolios containing options, futures andoptions on futures positions.

In particular, TIMS uses pricing models to project the liquidation valueof each portfolio given changes in the price of each underlying product.These models generate a set of theoretical values based on variousfactors including current prices, historical prices and marketvolatility. Based on flexible criteria established by a clearing house,statistically significant hedges receive appropriate margin offsets.TIMS also is used to predict a member's potential intra-day risk undervarying sets of assumptions regarding market behavior.

TIMS organizes all classes of options and futures relating to the sameunderlying asset into class groups and all class groups whose underlyingassets exhibit close price correlation into product groups. The dailymargin requirement for a clearing member is calculated based on itsentire position within a class group and various product groups. Themargin requirement consists of two components, a mark to marketcomponent and an additional margin component.

The mark to market component takes the form of a premium margincalculation that provides margin debits or requirements for net shortpositions and margin credits for net long positions. The margin debitsand credits are netted to determine the total premium margin requirementor credit for each class group. The premium margin component representsthe cost to liquidate the portfolio at current prices by selling the netlong positions and buying back the net short positions.

The additional margin component, the portion of the margin requirementthat covers market risk, is calculated using price theory in conjunctionwith class group margin intervals. TIMS projects the theoretical cost ofliquidating a portfolio of positions in the event of an assumed worstcase change in the price of the underlying asset. Theoretical values areused to determine what a position will be worth when the underlyingasset value changes. Given a set of input parameters (i.e., optioncontract specifics, interest rates, dividends and volatility), thepricing model will predict what the position should theoretically beworth at a specified price for the underlying instrument.

The class group margin interval determines the maximum one day increasein the value of the underlying asset (upside) and the maximum one daydecrease in the value of the underlying asset (downside) that can beexpected as a result of historical volatility. The methodology used todetermine class group margin intervals and product groups can bespecified by each clearing house. OCC's methodology for determiningclass group margin intervals is based on ongoing statistical analysis.For each class group, the standard deviation is computed and a margininterval is calculated which covers a predetermined percentage specifiedby the clearing house. This approach provides both a confidence leveland historical perspective on volatility and accounts for any non-normalprice distribution patterns. TIMS also calculates theoretical values atequal intervals between the two endpoints (upside and downside) and atthe current market value to protect against certain trading strategiesthat may have their largest loss between these two endpoints.

The methodology for determining which class groups comprise a productgroup and the appropriate percentage deduction to account for the lackof perfect correlation between class groups is also based on ongoingstatistical analysis. For each pair of class groups, TIMS computes acoefficient of determination. TIMS assigns class groups to a productgroup when the value of the coefficient between the class groups iswithin policy limits established by the clearing house. The productgroup percentage or offset is established based on the lowestcoefficient of determination among all of the class groups included inthe product group. When calculating an account's total marginrequirement, this specified percentage of any margin credits at theclass group level is used to offset margin requirements generated byother class groups in the same product group.

Yet another risk management system is the OMS II system, also referredto as the “Window method” or the “Vector method”. OMS II is the OM riskcalculation method for calculating margin requirements. It is includedin the risk valuation or RIVA system within OM SECUR. It was constructedin order to handle non-linear instruments in a better way than SPAN orTIMS. OMS II calculates worst case loss scenarios, stores these invectors, adjusts for spreading, and adds the vectors in a way that takescorrelation in to account.

In OMS II the valuation interval is divided into n (normally n=31)possible up or down moves, additionally for each up or down move thevolatility can either increase stand still or decrease. This gives us 93alternative market scenarios (if n=31) to calculate the profit or loss aportfolio will make.

The scenario with no price move at all is the middle scenario and aroundit there are 15 up and 15 down scenarios (or (n−1)/2 up and (n−1)/2 downscenarios).

TABLE OMS valuation scenarios. Underlying Price Volatility Scan RangeScan Range  1 Price unchanged Volatility down  2 Price unchangedVolatility unchanged  3 Price unchanged Volatility up  4 Price up 1/15range Volatility down  5 Price up 1/15 range Volatility unchanged  6Price up 1/15 range Volatility up  7 Price down 1/15 range Volatilitydown  8 Price down 1/15 range Volatility unchanged  9 Price down 1/15range Volatility up 10 Price up 2/15 range Volatility down 11 Price up2/15 range Volatility unchanged 12 Price up 2/15 range Volatility up 13Price down 2/15 range Volatility down 14 Price down 2/15 rangeVolatility unchanged 15 Price down 2/15 range Volatility up . . . . . .. . . 88 Price up 15/15 range Volatility down 89 Price up 15/15 rangeVolatility unchanged 90 Price up 15/15 range Volatility up 91 Price down15/15 range Volatility down 92 Price down 15/15 range Volatilityunchanged 93 Price down 15/15 range Volatility up (n = 31)

As in both SPAN and TIMS, one can view OMS II mathematically asproducing the maximum of the expected loss under each of 93 probabilitymeasures. For all 93 scenarios the probability measures are point massesat each of the 93 points in a space Ω of securities prices andvolatilities.

Each valuation point is saved in a 31×3 matrix, that is, each rowcontains a price move and the three volatility fluctuations. The matrixis expanded to a 31×6 matrix so that the case of both a bought and asold contract is represented in the matrix, this because of additionalfine-tunings that are available in OMS II. The matrixes are saved foruse when margin requirements of portfolios are calculated.

In the case of an account containing positions of two or more types ofcontracts the risk of the position is the combined risk characteristicsof the different contracts registered to the account. To take theoffsetting characteristics of the instrument into account one talksabout cross margining. The default cross margining divides the positionsinto one group per underlying. Positions on instruments within the sameunderlying are said to be totally correlated. The default cross margincan be described as instruments with the same underlying being totallycorrelated and instruments with different underlying being uncorrelated.During a default cross-margin run a portfolio with instruments on thesame underlying will add the valuation files pointwise as in SPAN andthen take the largest negative value as the margin requirement for theportfolio. If the portfolio consists of instruments on differentunderlyings the largest negative value of each valuation file will beadded.

However, a method such as default cross-margining does not takecorrelations between different underlyings or different expiry monthsinto consideration. Therefore in OMS II one uses the so-called “Windowmethod” when a portfolio containing instruments on different underlyingsor contracts with different expiry months is margined.

In the window method, the different instruments are sorted into a numberof groups, called window classes. The window classes have a window sizedefined in percent. When the percentage goes down the correlation goesup and vice versa, e.g. a window size of 0% means that the instrumentsin the window class are totally correlated and a window size of 100%means that the instruments in the window class are uncorrelated. Thereis also a possibility for a window class to be a member of anotherwindow class, and in such case creating a tree structure of morecomplicated correlations. To calculate the margin for a portfolio, thewindow is moved from left to the right over the entire valuationinterval for all window classes, starting with the ones in the bottom ofthe tree. The window is centered over each valuation point. A marginrequirement is calculated at each valuation point where the window ispositioned by adding the lowest value for each option position orfutures position shown in the window. The total margin requirement willbe the largest negative value of all these margin requirements. If thereis no negative value this indicates a credit and no margin is required.

The risk calculation part of OMS, without use of any fine-tunings,should also be a coherent risk measure, this since the calculations onlydiffer in the amount of scenarios used. OMS uses far more scenarios thenboth SPAN and TIMS.

A comparison of SPAN, TIMS and OMS II may be found in Bylund, Mattias,“A Comparison of Margin Calculation Methods for Exchange TradedContracts” (Feb. 21, 2002). Royal Institute of Technology Dept. ofMathematical Statistics, Master Thesis No. 2002-3.http://ssrn.com/abstract=300499, herein incorporated by reference. Whilethe disclosed embodiments will be discussed with reference to the SPAN®risk analysis software, it will be appreciated that they may also beapplicable to the TIMS risk analysis software, as well as other productsdirected at determining performance bond requirements and/or assessingrisk in a portfolio of derivatives.

The CME Clearing House requires “gross” performance bonds for customerpositions in CME products. The clearing member must deposit performancebonds for each open position (long or short) held at the end of eachday's trading, with appropriate allowances for spreads. A spread is theprice difference between two contracts, e.g., holding a long and a shortposition in two related futures or options on futures contract, with theobjective of profiting from a changing price relationship or theassumption of a long and short position on the same business day in thesame or related commodities for the same account. Long refers to one whohas bought a futures or options on futures contract to establish amarket position and who has not yet closed out this position through anoffsetting procedure, e.g. one who has bought a futures or optionscontract to establish a market position; a market position whichobligates the holder to take delivery; or one who owns an inventory ofcommodities. Long is the opposite of short.

A Spread order—Open Outcry: is an order that indicates the purchase andsale of futures contracts simultaneously. A Spread trade is thesimultaneous purchase and sale of futures contracts for the samecommodity or instrument for delivery in different months or in differentbut related markets. A spreader is not concerned with the direction inwhich the market moves, but only with the difference between the pricesof each contract.

Spreads include Bear spreads, Bull Spreads, Butterfly spreads, Calendarspreads and user-defined spreads. A Bear spread is a vertical spreadinvolving the sale of the lower strike call and the purchase of thehigher strike call, called a bear call spread. Also, a vertical spreadinvolving the sale of the lower strike put and the purchase of thehigher strike put, called a bear put spread. A Bull spread is a verticalspread involving the purchase of the lower strike call and the sale ofthe higher strike call, called a bull call spread. Also, a verticalspread involving the purchase of the lower strike put and the sale ofthe higher strike put, called a bull put spread. Butterfly spreads canbe futures or options spreads. As an option spread, a Butterfly spreadis a strategy combining a bull and bear spread and uses three strikeprices. The strike price is the price at which the option buyer maypurchase or sell the underlying futures contract upon exercise. Thelower two strike prices are used in the bull spread and the higherstrike price from the bear spread. Both puts and calls can be used. ACalendar spread, also known as a futures calendar spread or futuresintra-delivery spread, is the simultaneous purchase and sale of the samefutures contract, but for different contract months, for example, buyinga September S&P 500 futures contract and selling a December S&P 500futures contract. An options calendar spread is the simultaneouspurchase and sale of options of the same strike, but differentexpiration dates. User defined spreads relate to the ability to choosethe legs of a spread if the spread is not identified by Exchangealready.

In general, the purchase or sale of a futures contract is considered tobe an outright long or short position. However, another strategy knownas spread trading is also available to the hedger and speculator. Spreadtrading involves the simultaneous purchase of one commodity contractagainst the sale of another related contract. Natural spreadopportunities are available in the energy market between differentmonths of the same commodity contract, as well as between differentproducts and grades. Some players confine themselves to trading outrightfutures and options contracts, leaving the enormous potential of thespread markets untapped. This is primarily due to the misconception thatspreads are inherently more complex than outright positions. While therecan be additional risk holding both long and short positions indifferent commodity contracts, it is generally accepted that having aposition off-set by an equal but opposite position in another commoditycontract should lessen one's risk. This is reflected by the fact thatspread positions are less costly to margin than outright positions. Thehedger can benefit from the spread market as well. If spread values areclosely monitored, they can provide valuable information as to when andwhere a hedge should be placed.

There are four basic types of spreads. Though the most commonly tradedis the intramarket spread, they are all consistently played in the oilmarket.

-   -   1. Intramarket Spreads: This spread consists of a long position        in one contract month against a short position in another        contract month in the same commodity. For example: Buy April        Crude Oil—Sell May Crude Oil on the NYMEX.    -   2. Intermarket Spread: These spreads feature similar or related        commodities on different exchanges. For example: Buy April IPE        Gas oil—Sell April NYMEX Heating oil or Buy April IPE Brent—Sell        April NYMEX Crude oil. Strictly interpreted, this definition is        confusing when applied to the oil market, because spreads        between different commodities on the same exchange are sometimes        thought of as intermarket spreads.    -   3. Intercommodity Spreads: These spreads are comprised of a long        position in one commodity, and a short position in a different        but economically related commodity. For example: Buy April        Gasoline—Sell April Heating oil.    -   4. Commodity-Product Spreads: This can be defined as the        purchase of a commodity against the sale of an equivalent amount        of the product derived from it (or vice versa). In the oil        market, this is referred to as a “crack spread.” For example:        Buy 3 September Crude oil—Sell 2 September Gasoline+Sell 1        September Heating oil.

In theory, spread transaction is established in expectation that thedifferential between contacts will widen or narrow. Each side of thespread is referred to as a “leg.” If the trader buys the higher, morevaluable leg of the spread, he anticipates that the differential willwiden. Conversely, if he sells the higher leg, he believes it willnarrow. Whether the trader is long or short the spread depends upon whathe has done to the more valuable (premium) leg. This holds trueregardless of whether the market is at a carry or a discount.

For example: Assume November Crude oil is trading at $14.00, andDecember Crude oil is at $14.25. The trader buys the premiumleg—December, in belief that the 0.25 cent spread will widen (whilesimultaneously selling the November).

As the market gains in strength, November moves to $14.75, and Decemberto $15.50. To calculate the profit or loss, simply examine the profit orloss on each leg, and then the net result. In this example, the traderhas lost 75 cents on the short leg but has made $1.25 on the long leg.The result is a 50 cent net profit. Stated another way, the spread haswidened from 25 cents to a 75 cent differential. It is important to notethat the movement of the spread value is dependent upon the movement ofthe individual legs.

Spreading in Practice—Spread orders are normally placed by specifyingthe amount of difference between the two contracts of the spread, notthe price level of each contract. Without this latitude spread orderswould be impossible to fill because of the unlikelihood that bothcontracts would be at those exact prices at the same moment. The twomost common types of spread orders are “market” and “limit.” The marketorder would be the logical choice when spread values are unwavering andprompt execution is desired. If spread values are volatile, specificlimits on the differential should be stated. The simplest type of spreadorder to execute is the one between two months of the same commodity. Inthis case, values are easy to determine because they are quoted in thesame trading pit, much like an outright contract. Spreads betweendifferent commodities or exchanges are usually more difficult toexecute. It should be noted that it is rarely advisable to place orliquidate spreads one side at a time. This practice of “legging” spreadscan quickly turn a profitable trade into a loser. One should also avoidplaying spreads involving the nearest expiring contract unless there issubstantial liquidity remaining. A lack of liquidity can increase thepotential for loss, as it may mitigate or exaggerate spreaddifferentials. To determine the liquidity of a contract, simply comparethe open interest to that of the other contracts.

Basic Spread Strategies—A trader uses the same skills to determine thepotential of a spread as he would an outright position. Both technicaland fundamental factors may influence his decision to buy or sell aspread. Consequently, the technical relationship between potentialcontracts are weighed along with the effects of supply and demand. Thereis no general rule that says that a spread will offer greater profitpotential than an outright position, nor will it always be less risky.However, careful development of spread techniques can often translateinto large profits.

Carrying Charge Strategies—Since oil is a non-perishable commodity, themaximum premium that the distant months may sell over the nearby monthfor a prolonged period is limited to the cost of carry. If full carryingcosts are evident, very little risk, other than that created by changesin interest rates, is involved if your company sells the spread (longthe nearby—short the differed, in an ascending market). Widening of thespread, which would create losses, is limited, while there is no limitto the amount that the nearby can run over the backs. In a carryingcharge market, selling the nearby month and buying the distant, isusually not desirable. In that instance, the profit would be limited tofull carrying charges, and the loss could be unlimited.

Inverted Market Strategies—The fact that the oil markets are ofteninverted (with the nearby month at a premium to the distant months)presents interesting challenges to the spread trader. It is stillpossible to profit if changes in differentials can be predicted. In adiscount or inverted market, if one expects the discount to becomesmaller, the trader must sell the nearer and buy the distant contract.In order to profit when the discounts on the far months are expected toincrease, one must buy the front and sell the back.

Calculating SPAN requirements—i.e., the risk performance bond (margin)requirements obtained using the Standard Portfolio Analysis of Risksystem or the SPAN calculation algorithm, utilizing the disclosedembodiments, is described below in detail.

The SPAN algorithm has always been viewed as being applicable to anunlimited range of product types, but the original focus in itsimplementation has been on standardized futures, options on futures andoptions on physicals. Portfolios today, however, can contain the widestrange of derivative and non-derivative instruments. SPAN 4 supports theultimate in product flexibility using an advanced, object-orientedmodel. In particular, SPAN 4 adds support for equity securities and debtsecurities (stocks, bonds, etc.), and options thereon.

Despite these enhancements, the fundamentals of the SPAN calculation,and the principles behind them, have not changed. The underlyingsimplicity of SPAN has been preserved. The many new capabilitiesintroduced with SPAN 4 should be thought of not as changes to theunderlying methodology, but as providing a vastly greater degree offlexibility and control in the usage of SPAN.

Account types: Portfolios of positions to be margined using SPAN areheld in performance bond accounts, or margin accounts. The positions inan account constitute a single portfolio.

If this is a particular performance bond account of a clearing memberfirm at a clearing organization, we say that the SPAN calculation doneby that clearing organization for that account is a clearing-levelcalculation.

On the other hand, SPAN calculations may be done for particular customeror other accounts of firms which are clearing members, directly orindirectly, of one or more clearing organizations. These are firm-level,also called customer-level, calculations.

For any performance bond account, the account type is defined by:

-   -   whether this is a clearing-level account or a firm-level        account, and    -   the specific account type code—for example, member, hedger, or        speculator.

A business function represents a particular purpose for which anexchange or clearing organization using SPAN wishes to perform the SPANcalculation or have it performed, at either the clearing-level or thecustomer-level. For example:

-   -   Normal clearing-level calculation for a particular clearing        organization, applicable to normal clearing-level account types    -   Special member-clearing calculation for member clearing account        types    -   Normal customer-level calculation for the part of a portfolio        traded on, or cleared by, a particular exchange or clearing        organization    -   Clearing-level calculation for a particular cross-margin        agreement between clearing organizations    -   Customer-level calculation for a customer portfolio for a        particular cross-margin agreement

By definition, a clearing-level SPAN calculation for a portfolio isalways for a specific business function. In other words, the portfoliois identified with a specific business function, and may contain onlyproducts eligible for that business function.

By contrast, a customer-level portfolio may have any number of businessfunctions represented within the portfolio.

Business functions are also referred to in SPAN as exchange complexes,and the identifier for a business function as the exchange complexacronym. For example, CME represents the exchange complex acronym fornormal processing for the CME clearing organization

Requirement levels: For any particular business function representedwithin a portfolio, the exchange or clearing organization using SPAN maymandate the calculation of more than one SPAN requirement number. Eachsuch number is called a requirement level, and is specific to:

-   -   the performance bond class of the requirement level, and    -   the initial or maintenance designation of the requirement level.

Performance bond classes are used generically to designate differentlevels of SPAN requirements. The first class (the one with the lowestrequirement level) is specially designated as the core class and thesecond class (the one with the next-highest requirement level) as thereserve class.

Any number of performance bond classes can be defined, and for anypurpose. The most common purpose is to recognize different requirementlevels that may be met by different classes of collateral assets.Typically the core requirement must be met by the highest-qualityassets. The difference between the core requirement and the higherreserve requirement—the so-called reserve additional requirement—may bemet by certain lesser-quality assets.

Within the specific performance bond class, the exchange or clearingorganization using SPAN may mandate the distinction between the initialrequirement level and the maintenance requirement level. The initialrequirement is typically higher and applies to newly created portfolios.The lower maintenance requirement applies to previously existingportfolios. Typically this distinction is only made at thecustomer-level, and only for speculative customer portfolios.

Combined commodities: For each business function for which an exchangeor clearing organization is using SPAN, the set of products eligible forthat business function are grouped into combined commodities.

For each business function within a portfolio for which the SPANcalculation is being done, for each combined commodity representedwithin that business function, SPAN yields one or more SPAN riskrequirements. Each such requirement corresponds to a specific SPANrequirement level—a specific performance bond class and an initial ormaintenance designation.

SPAN requirements calculated for individual combined commoditiesrepresented in the portfolio are then aggregated to yield SPANrequirements for the different business functions represented within theportfolio, and for the entire portfolio.

The combined commodity may be thought of as the atomic-level of the SPANcalculation. It is the lowest breakdown of the products within aportfolio at which a performance bond requirement is obtained.

Typically, all products having the same underlying physical basis orcharacteristics are grouped together into a combined commodity—forexample, at the CME, all products related to the S&P 500 stock index.

Performance bond currencies: For each combined commodity, a singlecurrency is specified as the performance bond currency for that combinedcommodity.

This is the currency in which the performance bond requirement for acombined commodity represented within a portfolio, will be denominatedin.

Any number of performance bond currencies may be represented within theportfolio. Therefore, when aggregating SPAN requirements for thedifferent combined commodities represented within the portfolio, theseare typically first aggregated by performance bond currency.

These currency-level requirements may then be converted to a commoncurrency for further aggregation. This common currency is typicallycalled the native currency for the portfolio.

(The term “native currency” is used to reflect the fact that the desiredcommon currency may be different for different portfolios, typicallydepending on the national origin of the portfolio owner.)

SPAN risk parameter files: Clearing organizations and/or exchanges usingSPAN publish, at least once daily, one or more SPAN risk parameterfiles. For simplicity, these are typically referred to as SPAN files.

SPAN risk parameters may be generically defined as the set of dataneeded to calculate SPAN requirements, other than the actual portfoliosfor which the requirements are to be calculated. SPAN risk parametersconsist of (a) product data and (b) performance bond rate data. Ineffect, a SPAN risk parameter file contains SPAN risk parameter data inmachine-readable form.

Typically, SPAN risk parameter files contain data for exactly one pointin time. In effect, they contain data to be used for performance bondcalculations for portfolios existing at that point in time.

Within each point in time, the SPAN file contains data for one or morebusiness functions of the exchange or clearing organization publishingthe file. Within each business function, the file will contain data foreach combined commodity defined for the business function.

Ultimately, the file will contain many different SPAN rates—for example,risk arrays, intracommodity spread charge rates, intercommodity spreadcredit rates, etc. Each such rate is qualified by the account type andrequirement level to which it pertains.

For example, a risk array for a particular contract contained with atypical customer-level SPAN file may be designated as being for a hedgecustomer account, for the core performance bond class, and themaintenance requirement.

SPAN file formats previously in use only supported the inclusion of datafor exactly one point in time, business function, and rate—i.e., accounttype, performance bond class, and initial or maintenance designation.

The new XML-based SPAN file format does not have this limitation.

Point in time: Risk parameters and portfolios are defined at particularpoints in time.

Points in time are categorized as to whether they are for:

-   -   the end of day settlement, or    -   an intraday point in time.

Some clearing organizations, for some business functions, may publishmore than one SPAN file for the end-of-day settlement. These aretypically distinguished as being for:

-   -   the final settlement, or    -   an early (or preliminary) settlement, or    -   the complete settlement.

In the early settlement SPAN file, typically final end-of-day settlementprices are available only for some of the products, while other productshave intraday prices provided. The final settlement file typicallycontains final settlement prices for the day for all actively tradingcontracts. The complete file will contain final settlement prices forall contracts, actively trading or inactive.

An intraday point in time is further characterized by its businesstime—indicating the actual time to which prices and risk arrays pertain.A point in time, whether intraday or end of day, may also becharacterized by its run number—for example, the first intraday run, thesecond intraday run, etc.

Risk arrays, risk scenarios, composite deltas, scan points and deltapoints

Risk arrays: A risk array is a set of numbers, defined:

-   -   for a particular contract    -   at a particular point in time    -   to be margined for a particular business function    -   for a particular account type, and    -   for a particular requirement level—performance bond class and        initial or maintenance designation—for that account type.

Each risk array value specifies how a single long or short position willlose or gain value if the corresponding risk scenario occurs over thespecified look-ahead time. By convention, losses for long positions areexpressed as positive numbers, and gains as negative numbers.

The lookahead time: The lookahead time reflects the amount of time intothe future from the current time, for which the SPAN requirement levelsare intended to protect against declines in portfolio value. Lookaheadtime is a parameter of SPAN and may be set to any desired value. Thereare two methods, however, which are typically in use for itsspecification:

-   -   Actual time to the next business day: in this method, the number        of calendar days from the current business day to the next        business day is determined, and then divided by 365 days per        year, to obtain the lookahead time in years.    -   Average time per business day: in this method, the lookahead        time is typically set to one business day in a business year        assumed to have 250 business days per year, or 0.004 years.

Use of actual time to the next business day more closely protectsagainst the risk of larger changes in portfolio value over weekends andholidays, and may result in increased portfolio performance bondrequirements on the business day prior to a weekend, especially aholiday weekend. If, however, it is desired to avoid having theperformance bond requirement fluctuate merely because of weekends andholidays, use of average time per business day is more appropriate.

Risk Scenarios: Each risk scenario is defined in the following terms:

-   -   the (underlying) price movement    -   the (underlying) volatility movement, and    -   the weight, also called the covered fraction.

For futures, physicals and other non-option product types, these are theprice movement and volatility movement for the instrument itself. Foroptions, these are the price and volatility movements for the underlyinginstrument.

The values of the price movement, the volatility movement, and thecovered fraction are determined by the scan point definitions and thetwo scan ranges—the price scan range and the volatility scan range.These values are the key inputs to SPAN.

Scan point definitions: Each scan point definition consists of:

-   -   the price scan magnitude, as the number of price scan ranges up        or down—for example, 0.3333 or −2.000, meaning one third of the        price scan range up, or twice the price scan range down    -   the volatility scan magnitude, as the number of volatility scan        ranges up or down—for example, 1.0000 or −1.000, meaning the        full volatility scan range up or down    -   the weight.

The price scan magnitude may itself be expressed in terms of a pricescan numerator, a price scan denominator, and a price scan direction.For example, a price scan magnitude of −0.3333 may be expressed as anumerator of one, a denominator of three, and a direction of down.Similarly, the volatility scan magnitude may be expressed in terms of avolatility scan numerator, a volatility scan denominator, and avolatility scan direction.

SPAN 4 allows the definition, for each combined commodity of as manysets of scan points as may be desired, each for a different account typeand requirement level. The definitions must be identical, however, forsets of combined commodities which have intercommodity spreads definedamong them.

Calculation of risk array values: Generically, each risk array value iscalculated as:

-   -   the current value of the contract    -   less the hypothetical future value of the contract, after the        look-ahead time has passed, and (underlying) price and        volatility movements associated with the risk scenario have        occurred    -   multiplied by the weight.

For futures, physicals and certain types of combinations, this change invalue is determined by the price change alone.

To determine the hypothetical future value for options, the underlyingprice change, underlying volatility change, decrease in time toexpiration, and the associated interest rates must also be taken intoaccount, and a theoretical price calculated using an option pricingmodel.

In order to ensure that biases in the option pricing model do not affectthe result, the current value may also be calculated using the sameoption pricing model, assuming the current time to expiration, currentunderlying price, and current underlying volatility. In other words, therisk array value for an option is determined by subtracting thehypothetical future theoretical value of the option, from the currenttheoretical value of the option.

The actual model selected, the parameters of the model, the interestrates, and the look-ahead time are all parameters of SPAN.

The composite delta, and delta point definitions: The composite deltavalue is associated with each risk array defined for a contract. Thecomposite delta is a probability-weighted average of a set of deltascalculated for the contract (a) after the look-ahead time has passed and(b) according to the scenarios defined by the definition of the deltapoints.

Delta points are defined exactly analogously to scan points, with aprice scan magnitude, a volatility scan magnitude, and a weight.Suppose, for example, that there are seven delta points defined. Sevendelta values are calculated for the contract, using the price scanmagnitude and the volatility scan magnitude associated with each deltapoint, and assuming that the look-ahead time has passed. A weightedaverage of these deltas is then taken; using the weights specified inthe delta point definitions.

In effect, a composite delta value represents an estimate of what thecontract's delta will be after the look-ahead time has passed.

Overall SPAN process: To calculate SPAN requirements for a particularportfolio defined at a particular point in time, in which particularbusiness functions for particular exchanges or clearing organizationsare represented:

-   -   Obtain the applicable SPAN risk parameter file(s).    -   Using the positions in the portfolio, and the data contained in        the SPAN files, apply the SPAN algorithm.

This yields the SPAN requirement:

-   -   for the specific account type    -   for each combined commodity of each business function        represented in the portfolio    -   and for each combined commodity, for each applicable requirement        level (performance bond class, initial or maintenance        designation).

Determining the set of requirement levels to be calculated for aportfolio; direct and indirect calculation: For a combined commodity ina portfolio of a particular account type, it is necessary to select theset of performance bond requirement levels—i.e., unique combinations ofperformance bond class and initial or maintenance designation—for whichSPAN requirements should be calculated, directly or indirectly.

A directly calculated SPAN requirement is a requirement, at a particularperformance bond requirement level, for which the full SPAN calculationis done—i.e., scanning, spreading, etc.

An indirectly calculated requirement is one that is derived from anotherrequirement, at a different requirement level, by the application of asimple multiplicative scaling factor. Indirectly calculated requirementsare also known as derived requirements.

The selection of the set of requirement levels to be directlycalculated, for a particular combined commodity in a portfolio, isdriven by the set of requirement levels represented in the risk arraysfor the products in that combined commodity. In particular, this isdriven by which set of requirement levels are present for which accounttypes.

If there are risk arrays for this combined commodity for the particularaccount type of the portfolio, then these are the ones that determinethe requirement levels to be directly calculated.

For example, suppose the portfolio is for a hedge customer, and in theSPAN file for a particular combined commodity in the portfolio, one setof risk arrays is provided for hedge customers—specifically, for thecore maintenance requirement level. In this case one SPAN requirementlevel should be directly calculated—the hedge customer core maintenancelevel.

On the other hand, suppose there were risk arrays for two requirementlevels for this account type—for core maintenance and for core initial.In that case we would directly calculate separate SPAN requirements forthese two levels.

On the other hand, if there are no risk arrays for this portfolio'saccount type, then one of the other account types for which risk arraysare present is selected, and SPAN requirements are calculated for thelevels defined for this selected account type.

Risk adjustment factors and derived requirements: For each combinedcommodity, any number of risk adjustment factors may be provided in theSPAN risk parameter file.

Risk adjustment factors may be used either to adjust requirements atdirectly calculated risk levels, or to derive requirements at other risklevels (indirect calculation.)

Each risk adjustment factor has the following defined for it:

-   -   the account type to which it pertains    -   the base requirement level, i.e., the requirement        level—performance bond class and initial or maintenance        designation—which will be used to derive another one    -   the target requirement level—the requirement level being        adjusted or derived    -   the value of the factor

To apply a risk adjustment factor, simply multiply the requirement atthe base level by the value of the factor.

Adjustment factors used to derive an initial requirement for aparticular performance bond class from a maintenance requirement forthat class are also known as initial to maintenance ratios.

The SPAN calculation, summarized:

A directly-calculated SPAN requirement at a particular requirement levelfor a combined commodity in a portfolio is calculated as:

-   -   Sum the scan risk, the intracommodity spread risk, and the        delivery (spot) risk.    -   Subtract the intercommodity spread credit.    -   Take the larger of this result, and the short option minimum.

The scan risk is the risk for a combined commodity in a portfolioassuming perfect correlations in price and volatility movements of theunderlying instruments over time.

The intracommodity spread risk allows the recognition of risk associatedwith spreading within the combined commodity—so-called calendarspreads—for combined commodities where there is imperfect correlation ofprice and volatility movements over time, and allows precise targetingof these requirements to particular intracommodity strategies.

The delivery, or spot risk, recognizes the unique risk characteristicsof physically deliverable products, and of derivatives based on suchphysically deliverable products, as they approach the delivery period orgo through the delivery process.

The intercommodity spread credit provides appropriate creditsrecognizing risk offsets between positions in the different combinedcommodities represented in the portfolio.

The short option minimum recognizes the unique characteristics of shortoption positions, and allows the recognition of a minimum risk value fordeep out-of-the-money short options.

The sum of the scan risk, intracommodity spread risk, and the deliveryrisk is often referred to as the commodity risk, i.e., it is the riskfor the combined commodity in the absence of any credits forintercommodity spreading.

The result obtained by subtracting the intercommodity spread credit fromthe commodity risk is often referred to as the pre-SPAN risk. This valueis the directly calculated SPAN requirement, assuming that the shortoption minimum requirement is less.

Products supported in SPAN: SPAN supports the widest possible range ofderivative and non-derivative product types. There is no product typethat cannot be margined using SPAN.

Product terminology: The terms contract and product are used hereininterchangeably to refer to a specific tradable instrument—physical ornot, derivative or not—in which positions to be margined may be held.

Clearing organizations, exchange groupings, and product families

At the highest level, products are cleared by clearing organizations.

Each clearing organization may have one or more exchange groupingsdefined for it.

Within each exchange grouping, products are grouped into productfamilies.

Generally, a product family is identified within an exchange grouping bya product code—an alphanumeric value, for example, SP at the CME forproducts related to the S&P 500 stock index—and a product type—forexample, futures, options on futures, etc.

Each product family is also assigned a product family ID number that isunique within the clearing organization and may be unique within theexchange grouping.

Product families may be defined in as specific a manner as desired. Forexample, at the CME, other parameters used to make product familiesunique include the settlement method (cash-settled or physicallydeliverable), the valuation method (futures-style or equity-style), thesettlement currency, and, for options, the exercise style (American orEuropean). Contract size may also be used to as a factor, which definesseparate product families, although SPAN also supports the inclusion ofcontracts of different sizes in the same product family.

Contracts: In SPAN, tradable instruments, whether derivative ornon-derivative, are generically referred to as contracts or as products.As described above, contracts are grouped together in product families,and product type is always one of the things that makes a product familyunique.

Product types and underlying product types: SPAN 4 allows the creationof any number of product types. Product types may be for physicals orderivatives and, if the latter, for combination or non-combinationproducts.

Each contract (product) which is not a physical of one or another typeis classified as a derivative, and has one or more underlying contracts.

Derivative products that have exactly one underlying contract are knownas non-combination derivatives.

For example, a futures contract has a single underlying contract, calledthe underlying physical. An option on a future has a single underlyingcontract, the underlying future. An option on a physical has a singleunderlying contract, the underlying physical.

Derivative contracts that have two or more underlying contracts aregenerically known as combinations. Each such underlying is referred toas a leg of the combination.

For example, a combination, which is a futures calendar spread, wouldhave two underlying contracts—the futures contract which is the frontcontract of the spread, and the futures contract which is the backcontract of the spread.

At this time, SPAN recognizes three subtypes of the generic physicaltype: equity securities, debt securities, and debt securities marginedon an equivalent basis.

Swaps, repos and reverse repos are recognized as subtypes of thecombination type.

Contract structure and contract underlying ratios: The set of underlyingcontracts for a derivative product is known as its contract structure.Each element in the set specifies:

-   -   the specific underlying contract    -   the underlying ratio for this specific underlying contract.

Underlying ratio may be defined as follows:

-   -   For any contract X which is not a physical:        -   For each of its underlying contracts Y_(i):            -   The underlying ratio is the number of units of that                underlying Y_(i) which are bought (or sold) per one long                position of the contract X, expressed as a positive                number if buying, or a negative number if selling.

In other words, the underlying ratio tells you:

-   -   whether buying the derivative means buying or selling this        specific underlying contract, and    -   how many of this specific underlying are bought or sold per        purchase of one derivative contract.

For example, the contract structure for a futures butterfly spread wouldspecify that buying one spread means buying one of the first future,selling two of the second future, and buying one of the third future.

For example, a call option on 100 shares of stock. If you hold one longposition in this call, and you exercise it, you receive (purchase) 100shares of stock. Hence the underlying ratio is +100. On the other hand,if you own a put option on 100 shares of stock, and you exercise it, youdeliver (sell) 100 shares of stock. Hence the underlying ratio for thisput option is −100.

Contract Price and Contract Value Calculations: Every contract, at everypoint in time, has a contract price associated with it.

For exchange-traded instruments, for SPAN being used as an end-of-daytool for calculating performance bond (margin) requirements, this willbe the end-of-day settlement price.

At other points in time—for example, during the trading day—this may bean intraday theoretical price.

SPAN uses the price of a contract to determine the monetary value of asingle position in that contract—the contract value. This monetary valueis expressed in the settlement currency for the contract, also calledthe price quotation currency.

To calculate contract value multiply the contract price by the contractvalue factor for the contract. The contract value factor is themultiplier, which converts a quoted price for the contract into itsmonetary value in the contract's settlement currency.

(The contract value factor can in turn be derived from the specificationof the contract size and the convention used for quoting prices. Forexample, for the CME's live cattle futures contract, the contract sizeis 40,000 pounds and the price is quoted in dollars per 100 pounds.Hence the contract value factor is 40,000/100=400.)

Contract periods: The concept of contract period is used in SPAN todenote products with different maturities or expirations. Contractperiod can be thought of as a generalization of the contract monthconcept.

All contracts (except those that are margined on an equivalent basis)have a contract period code defined. Contract period codes may be six,seven, or eight bytes in length. The first six bytes consist of numericdigits. The seventh and eighth bytes, if defined, may consist of anyalphanumeric character. A contract period code has the followingstructure:

-   -   the four-digit year number—for example, 1999    -   the two-digit month number—for example, 05 for May    -   if needed, a two-byte string which may be used to further        qualify the contract period.

Option Series: An option series in SPAN 4 consists of all options withthe same expiration and the same underlying.

Standard options within a series, then, differ from each other only intheir strike price and their option right—i.e., whether they are puts orcalls.

For more exotic options, such as barrier options, they may also bedistinguished by one or more barrier prices.

Participation of product families in business functions: A productfamily is said to participate in a particular business function, if ithas been assigned to one of the combined commodities defined for thatbusiness function.

Every product family always participates in the normal clearing businessfunction for its clearing organization. It may, but is not required to,participate in additional business functions.

Combined commodities and delta periods: The products assigned to acombined commodity determine an array of delta periods defined for thatcombined commodity. Each contract is mapped into a specific deltaperiod, and delta periods in turn are mapped into tiers.

Tiers and Tiered Processing: A tier in SPAN is a contiguous range ofdelta periods within a combined commodity.

To provide the utmost flexibility, tiered processing is supported inSPAN 4 for:

-   -   scan rate tiers—the specification of tiers for defining price        scan ranges and volatility scan ranges    -   scanning tiers    -   intracommodity spread tiers    -   intercommodity spread tiers    -   short option minimum rate tiers

Specific tiers of a particular type for a combined commodity are alwaysidentified by a tier number beginning with one, and are furtherqualified by a beginning period code and an ending period code. Theending period code must be greater than or equal to the beginning periodcode, and the delta periods for the different tiers never overlap.

For intra- and inter-commodity spreading, sometimes there are caseswhere more than one tier is defined, but it is desired in a particularleg of a spread to reference the entire combined commodity, across alltiers. To support this, SPAN recognizes for each combined commodity anintracommodity spread tier zero and an intercommodity spread tier zero,which are defined as the range of period codes for the entire combinedcommodity, crossing individual tiers. This may also be referred to asthe overall tier.

One important aspect of SPAN 4's flexibility is the ability for scanningtiers and intercommodity spreading tiers to be defined independently.Previously there were limitations on this ability.

Mapping each delta period into its tier

For a given tier type for a combined commodity, to determine the tierinto which a delta period maps:

-   -   Compare the delta period code with the beginning period and the        ending period.    -   If the delta period code is greater than or equal to the        beginning period, and less than or equal to the ending period,        then it maps into that tier.

Portfolios to be margined: As described above, a portfolio of positionsto be margined using SPAN is held in an account. Each such account has aspecific account type.

Portfolios may be defined at either the clearing-level or thecustomer-level. In other words, they are either for a specificperformance bond account of a clearing member firm of a clearingorganization, where the margin calculation is being done by thatclearing organization, or they are for a specific customer-level accountof a member firm or other trading firm, where the margin calculation isbeing done by that firm.

A clearing-level portfolio always holds positions for a single businessfunction of that clearing organization, while any number of businessfunctions and clearing organizations may be represented in the positionsfor a customer-level portfolio.

Position definition: A position within a portfolio to be margined at aparticular point in time, is defined by:

-   -   the point in time at which the portfolio exists    -   the portfolio in which the position is contained, specified as        the firm identifier, the account identifier, the account type        (including whether this is a clearing-level or firm-level        account), and the segregation type    -   the contract in which the position is held, and the business        function for which the contract is to be margined, and    -   the position quantity number(s).

For example, a particular position might be defined as:

-   -   the end-of-day settlement for Dec. 1, 1999    -   firm 322, account XYZ, account type hedge customer, and        segregation type OUST (for Customer)    -   the CME's December 1999 S&P futures contract, to be margined for        the normal business function, and    -   a net position of +17.

Gross and net position keeping: A gross position is one that may besimultaneously long and short. A net position is one that is neversimultaneously long and short.

In other words, a net position is one that is determined by nettingtogether the beginning position for the day with all buys and sells forthat day. For net positions, all trades are liquidating to the extentpossible.

A gross position is determined by the beginning of day position and, foreach trade done for that day, whether it was an opening (new) or closing(liquidating) transaction.

At the firm-level, accounts are commonly kept net, with two typicalexceptions: (1) omnibus accounts, discussed below, and (2) certain typesof hedger accounts.

At the clearing level, positions are typically kept gross for accountswhich themselves are aggregates of more than one account at the firmlevel, in order to reflect true open interest.

Net margining: At the firm-level and often at the clearing-level,portfolios are typically “net margined.” This is also typically called“calculating a net requirement.” This means two things:

-   -   If the position is kept gross—i.e., if the position may be        simultaneously long and short—then it is first netted before        being processed in SPAN. Only the portfolio of net positions is        margined.    -   No restrictions are placed on the recognition of risk offsets        between different parts of the portfolio.

Since SPAN does recognize all allowable risk offsets, as they aredefined in the SPAN risk parameter file and as they are present in theportfolio, “net margining” translates into, process a portfolio of netpositions via SPAN.

Note that there is a distinction between gross and net position keeping,and gross and net margining: A position may be simultaneously keptgross, while being margined net. This is sometimes the case for certaintypes of hedge customer accounts.

Omnibus accounts and levels of disclosure; gross margining at the firmlevel: An omnibus account is an account of one firm on another firm'sbooks, which account is itself comprised of a number of individualaccounts on the first firm's books. The firm with the omnibus account issaid to carry the omnibus account on its books, and is often called the“carrying firm.” The individual accounts on the first firm's books aresaid to be “subaccounts” of the omnibus account.

Because an omnibus account is comprised of any number of subaccounts,omnibus account positions must be kept gross. Any given position in anyomnibus account may itself be the sum of a number of subaccountpositions, some of which may be long and some of which may be short.

If the omnibus account is “fully disclosed” to the carrying firm whichmust calculate a margin requirement for it, this means that it hasinformed the carrying firm of each individual subaccount and what itspositions are. Depending on business practices, this may not mean thatit has identified the owner of each subaccount, but rather simply thatit is has specified which sets of positions belong to single owners.

In this case, the carrying firm typically calculates a net requirementfor each subaccount, and the total omnibus account requirement is simplythe sum of the subaccount requirements.

On the other hand, an omnibus account portfolio may be only “partiallydisclosed”, or “non-disclosed.”

If partially disclosed, the omnibus account has provided information tothe carrying firm about some sets of subaccounts, but not of all. Ifnon-disclosed, no information is provided about the subaccounts andwhich positions they hold.

The portion of each gross omnibus account position which is not held indisclosed subaccounts, is typically said to be “naked”. In other words,for each position—total long and total short—there is a nakedportion—the naked long and naked short.

These naked positions are typically “gross margined.” This means that:

-   -   A separate SPAN requirement is calculated for each naked long        position quantity, and for each naked short position quantity.        Because each such position quantity is in a single contract, and        is only on one side of the market, there are no risk offsets        recognized in such requirements.    -   The total requirement for the naked portion of the account        portfolio is the sum of all of these individual naked long and        naked short requirements.

If the omnibus account is partially disclosed, its total requirement isthe sum of all of the net requirements for the subaccounts, plus the sumof all of the individual naked long and naked short requirements for thenaked positions.

Gross-margining at the clearing level: At the clearing-level, theoverall term “gross margining” is used to refer to a business practicewhere:

-   -   Positions are kept gross—i.e. may be simultaneously long and        short.    -   Some portion of the total long and total short for each position        is broken out, and margined net. This portion is termed the        fully inter-commodity spreadable long and short, and is often        referred to as the “intercommodity spreadable” or the        “inter-spreadable” long and short, or as just the “inter        positions.”    -   Another portion of each total position is broken out, and        margined net, except that no risk offsets are recognized among        the different combined commodities in the portfolio—i.e., no        intercommodity spreading is done. This portion is termed the        “intracommodity spreadable”, the “intra-spreadable” or as just        the “intra positions.”    -   The remaining portion of each total position is considered        naked, and margined gross.

We say that some portion of the total positions has been deemed to bespreadable both within commodities and between commodities, anotherportion to be spreadable only within commodities but not betweencommodities, and that a final portion to be spreadable not at all. Thetotal SPAN requirement for each combined commodity in the clearing-levelportfolio is then determined from the various components of the SPANrequirements calculated for these different position types.

So at the clearing-level, “gross margining” doesn't mean that positionsare fully gross margined, but rather that some portion of the overallpositions may be.

Clearing-level gross margining is typically used for customer-originperformance bond accounts where the clearing-level positions aredetermined by aggregating positions across many individual customeraccounts. Typically, the positions within each customer account areinspected to determine whether risk offsets exist both within andbetween commodities, or only within commodities, or not at all. Based onthis inspection, the customer's positions are classed asinter-spreadable, inter-spreadable, or naked. The total clearing-levelinter-spreadable long and short positions, then, are calculated as thesum of the customer positions that were classed as inter-spreadable, andanalogously for the intra-spreadable positions.

Position accounts, performance bond accounts, margin dispositions, andpositions to be margined

At the clearing-level, it is possible for a distinction to be drawnbetween the position accounts in which positions are kept, and theperformance bond accounts in which they are margined.

In this case, there may be a great deal of flexibility in how positionsroll up from position accounts to performance bond accounts.

For example, positions in products eligible for participation in aparticular cross-margin agreement may be routed to a performance bondaccount specifically for that cross-margin business function, whereaspositions in other products, not eligible for this cross-marginagreement, are routed to a performance bond account specified as beingfor the normal business function.

Even within a particular position, if that position is eligible for morethan one business function, the position itself may be broken down intoany number of “positions to be margined”, or “dispositions”, each ofwhich is designated for a particular performance bond account and henceto be margined via the SPAN parameters for a specific business function.

For example, a total gross position of 100 long and 200 short in aproduct eligible for a particular cross-margin agreement, might havedispositions for it of 50 long and 75 short for the cross-marginbusiness function, and 50 long and 125 short for the normal businessfunction.

Within each disposition, the position-to-be-margined may be marginedeither “gross” or net. If “gross”, each total position-to-be-margined isfurther broken down into an inter-spreadable long and short, anintra-spreadable long and short, and a naked long and short. If “gross”,as described above, the inter-spreadable positions are margined net, theintra-spreadable positions are margined net but without allowingintercommodity spreading, and the naked positions are truly marginedgross.

The SPAN calculation for net portfolios: This section contains thedescription of the detailed algorithm for calculation of a SPAN riskrequirement for each combined commodity represented in a portfolio to bemargined on a net basis—a so-called “net portfolio.” This may be eithera customer-level portfolio or a clearing-level portfolio.

Position processing: Position processing in SPAN consists of processingeach position within each combined commodity represented in theportfolio, for the purposes of:

-   -   Scanning: scaling up the risk array(s) for the contract by the        position quantity, and incrementing the overall risk array(s) by        these scaled-up risk array(s)    -   Delta calculation: scaling up the SPAN composite delta(s) for        the contract by the position quantity, and incrementing the        overall position delta(s) for the associated delta period by        these scaled-up composite delta(s)    -   Short option minimum calculation: determining the effect of the        position on the quantity for determination of the short option        minimum charge (also called the minimum commodity charge).    -   Position value calculation: evaluating the current monetary        value of each position, and incrementing the overall current        monetary values for the combined commodity, broken out by        whether the position is long or short and by whether the        contract is valued futures-style or premium-style.

Position types for the position value calculations: Products can becategorized by whether their valuation method is futures-style orpremium-style:

-   -   For futures-style products, there is a daily mark-to-market for        open positions, and the resulting settlement variation amounts        are paid or collected daily.    -   For premium-style products, the full trade price (premium) is        paid or collected when the position is opened.

Futures contracts, of course, are valued futures-style; the daily markto market and the daily payment or collection for settlement variation(sometimes called “variation margin”) is what distinguishes them from aforward contract.

Option positions are typically valued premium-style, but someexchange-traded options are valued futures-style.

The significance of whether a position is valued premium-style is asfollows: If a position is valued premium style, and if the full value ofthe premium is considered to have been paid (or collected), then thecurrent value of the position is counted as a collateral asset (if long)or a liability (if short).

For the positions in each combined commodity represented in theportfolio, then, it is necessary to determine the value of thosepositions broken out the following ways:

-   -   by whether the positions are valued futures-style or        premium-style    -   by whether the position quantities are long or short    -   by whether the positions are in options or are not in options.

In other words, for each combined commodity in the portfolio, we willhave determined:

-   -   value of long non-option positions in products valued        futures-style    -   value of short non-option positions in products valued        futures-style    -   value of long option positions in products valued futures-style    -   value of short option positions in products valued futures-style    -   value of long non-option positions in products valued        premium-style    -   value of short non-option positions in products valued        premium-style    -   value of long option positions in products valued premium-style    -   value of short option positions in products valued premium-style

Note that in some cases, the exchange or clearing organization usingSPAN may establish a business rule regarding the timing of therecognition of value for premium-style products. For example, suppose anunsettled trade for a stock done for the current business day isincluded in the portfolio of positions to be margined, and that thistrade will settle three days subsequently. In this case, the clearingorganization might decide not to give full or even partial credit forthe premium value of this trade until it has settled and the fullpremium has been paid or collected. If so, the total premium value usedfor the purpose of determining whether a margin excess or deficitexists, should be adjusted by the amount of this premium value for whichcredit is not being given.

Special position-processing features: In addition to regular positionprocessing, SPAN supports several special position-processing featureswhich provide additional power and flexibility:

-   -   Split Allocation is typically used for positions in combinations        and/or options on combinations where the underlying instruments        of the combination are in different physical commodities. With        this feature, the position in the combination or the option on        the combination, is split out (allocated) into positions on the        underlying instruments of the combination.    -   Delta-Split Allocation is typically used for positions in        combinations and/or options on combinations where the underlying        instruments of the combinations are at different expirations        within the same physical commodity. This is similar to regular        split allocation, but differs in that only the delta from the        position in the combination or the option on the combination, is        split out to the delta periods of the underlying legs.    -   Equivalent Positions is used when it is desired to margin a        position in one instrument, as one or more equivalent positions        in other instruments.

Expression of Net Position Numbers: For positions in a net portfolio,position quantities are expressed as signed numbers, positive for a netlong position, and negative for a net short position.

Depending on the types of instruments in the portfolio and theconventions used for expressing their positions, it is possible forposition quantities to be fractional—i.e., not whole numbers.

Pre-Processing for Margining Debt Securities on an Equivalent Basis: Forpositions in physical debt securities, which are being margined on anequivalent basis, it may be necessary to perform special pre-processingto express the position quantities properly, even before thetransformation of the debt securities position into its equivalents.This section describes that pre-processing.

For government debt securities to be margined on an equivalent basis,positions should be expressed in units of thousands of par valuecurrency units in the currency of denomination. For example, a positionin a U.S. Treasury Bond with a face value of $1,000,000 should beexpressed as 1,000.

Positions to be margined in such physical debt securities are thoseresulting from not-yet-settled trades. The actual position in suchsecurities can sometimes be broken out as the sum of:

-   -   the net position from open outright trades, and    -   the net position from open repos (or reverse repos) in which the        on-leg has settled but the off-leg has not yet settled, with a        net repo position expressed as a positive number and a net        reverse repo position expressed as a negative number. Such repos        are referred to as same-day repos when they are entered into        (and margined), since on the day they are entered into, the        on-leg settles, leaving only the unsettled off leg to be        margined.

Repo and reverse repo positions where neither leg has settled aretypically considered to be next-day repos. In other words, the repo isentered into today, with the on-leg beginning tomorrow. Since the on-legand the off-leg are both not-yet-settled, these obligations cancel eachother out. So these next-day repo or reverse repo positions are notincluded in the margin calculation.

Processing Split-Allocation Positions: After transforming any positionsto be processed on an equivalent basis into their equivalents, the nextstep in position processing is to deal with any positions that are to behandled using the split allocation method.

As described above, split allocation is typically used for positions inoptions on futures intercommodity spreads. The method is genericallyapplicable, however, to any combination product or option on combinationproduct.

The specification of whether split allocation is to be performed is donefor a product family linked into a combined commodity. Not all productfamilies linked into a combined commodity need be processed using splitallocation. In general, however, for the algorithm to yield the desiredresults, split allocation should be specified for both the options onthe combination, and the combination itself. Typically both of theseproduct families will be placed into the same combined commodity.

Determining position quantities for further processing: With positionsto be processed on an equivalent basis transformed into theirequivalents, and positions to be processed via split allocation,allocated out to their underlyings, we're now ready to determine theposition quantities to be carried forward in SPAN.

The following applies to all position types except positions processedon an equivalent basis. (As explained above, such positions play noadditional role in the calculations once they have been transformed intotheir equivalents.)

The algorithm will evaluate five different values for each position:

-   -   the total position    -   the marginable position    -   the position for valuation    -   the position for scanning    -   the positions for the short option minimum calculation—the        number of short calls and the number of short puts

For each position in the portfolio:

-   -   The total position is equal to the sum of the position in the        contract itself, the equivalent position, and the position        resulting from split allocation.    -   The marginable position is equal to the total position times the        contract-scaling factor.    -   The position for valuation is the sum of the position in the        contract itself and the rounded position resulting from        equivalents.    -   The position for scanning is determined as follows:        -   If the product family for this position is processed either            normally or via delta-split-allocation, take the marginable            position.        -   If the product family for this position is processed via            split allocation, take zero.    -   The positions for the minimum commodity charge are determined as        follows:        -   If this position is not for an option, then the number of            short calls and the number of short puts are both zero.        -   But if this position is for an option:            -   If the marginable position is zero or positive, then the                number of short calls and the number of short puts are                both zero.            -   But if the marginable position is negative:                -   If the option is a call, the number of short calls                    is equal to the absolute value of the product of the                    marginable position and the delta-scaling factor.                    The number of short puts is zero.                -   If the option is a put, the number of short puts is                    equal to the absolute value of the product of the                    marginable position and the delta-scaling factor.                    The number of short calls is zero.

Determining the Position Value: For each combined commodity in theportfolio:

-   -   For each position in the portfolio:        -   Take the position for valuation as determined above.        -   Multiply this result by the value of a single contract,            yielding the value of the position in the settlement            currency for the contract.        -   If the performance bond currency for the combined commodity            in which the product is contained is different from the            settlement currency of the product, convert the value from            the settlement currency to the performance bond currency,            rounding as may be needed to the normal precision of the            performance bond currency. This yields the value of the            position in the performance bond currency for the combined            commodity.

Determining the Liquidation Risk Position Value: The Liquidation Riskcalculation is a method of determining the Scan Risk, which has beenintroduced in SPAN for the Paris Bourse (SBF.) This calculation requiresthe determination of a special position value called the LiquidationRisk Position Value. As can be seen, this differs from the regularposition value in that (a) it includes any position quantity resultingfrom split allocation, and (b) for positions in debt securities, it isadjusted for the duration of the security.

For each combined commodity in the portfolio for which “liquidationrisk” has been specified as the method for determining the scan risk:

-   -   For each position for products linked into this combined        commodity:        -   Take the position for scanning, as determined above.        -   If this position is in a debt security, multiply this value            by the duration of that security, expressed in years.        -   Multiply this result by the value of a single contract.        -   If the performance bond currency for the combined commodity            in which the product is contained is different from the            settlement currency of the product, convert this value from            the settlement currency to the performance bond currency.        -   Round this result as specified. (The rounding convention            used by SBF for liquidation risk position value is to round            down—toward zero—to five decimal places.) The result is the            liquidation risk position value.

Determining the Currency Conversion Rates for the Intercurrency RiskScanning feature of the Scan Risk calculation: Intercurrency riskscanning is an optional feature of the scan risk calculation which maybe applied in cases where there are products whose settlement currencyis different from the performance bond currency of the combinedcommodity into which they are linked.

When a product family is linked into a combined commodity, it may bespecified that intercurrency risk scanning is applicable.

If intercurrency risk scanning is specified, then the risk array valuesfor that product family linked into that combined commodity aredenominated in the settlement currency for that product family.

For each such settlement currency and performance bond currency pair, itis necessary to determine the exchange rate up and the exchange ratedown:

-   -   For a given settlement currency and performance bond currency        pair, read the intercurrency scan rate up and the intercurrency        scan rate down. (These are provided in the London format SPAN        file on the currency conversion rate record for that currency        pair.) Express these values as decimal fractions. If the        settlement currency is equal to the performance bond currency,        take zero for these values.    -   Take the exchange rate multiplier, which converts a value in the        settlement currency to one in the performance bond currency. If        the settlement currency is equal to the performance bond        currency, take one for this value.    -   Multiply the exchange rate by the value of one plus the        intercurrency scan rate up, yielding the exchange rate up.    -   Multiply the exchange rate by the value of one minus the        intercurrency scan rate down, yielding the exchange rate down.

Determining the Scaled-Up Risk Array(s) and Delta(s) for the Position:For each combined commodity in the portfolio for which scanning is beingperformed normally (not using the “liquidation risk” scanning method):

-   -   For each product family in this combined commodity:        -   For each position in this product family:            -   Take the position for scanning as determined above.            -   For each directly calculated requirement level for this                portfolio type and combined commodity:                -   Take the risk array for this product as linked into                    this combined commodity and for this requirement                    level.                -   Multiply each element in the risk array by the                    position for scanning, yielding the scaled-up risk                    array for the position.                -   If the intercurrency risk scanning feature is                    enabled for this product family:                -   Multiply each element in the scaled-up risk array by                    the exchange rate up for this settlement                    currency/performance bond currency pair, yielding                    the scaled-up converted-up risk array.                -   Multiply each element in the scaled-up risk array by                    the exchange rate down for this settlement                    currency/performance bond currency pair, yielding                    the scaled-up converted-down risk array.                -   To determine the position delta:                -   Take the composite delta for this product as linked                    into this combined commodity and for this                    requirement level.                -   Multiply the position for scanning by the composite                    delta and then by the delta-scaling factor.

Aggregation of position values to the combined commodity: For eachcombined commodity in the portfolio:

-   -   For each position in the combined commodity:        -   Take the position value as calculated above.        -   Using the position value, increment one of eight value            buckets for the combined commodity determined according to            whether:            -   The position value is long (positive) or short                (negative).            -   The position is for an option or a non-option.            -   The position is valued futures-style or premium-style.

Aggregation of short option positions: For each combined commodity inthe portfolio:

-   -   For each position in the combined commodity:        -   For each short option minimum rate tier for the combined            commodity:            -   Increment the number of short calls for the overall tier                by the number of short calls for the position as                calculated above.                -   Increment the number of short puts for the overall                    tier by the number of short puts for the position as                    calculated above.

Determining the Number of Short Option Positions for a Tier: If theshort option minimum charge method for the combined commodity is gross:

-   -   Take the sum of the number of short calls for the tier and the        number of short puts for the tier.

If the short option minimum charge method for the combined commodity ismaximum:

-   -   Take the larger of the number of short calls for the tier and        the number of short puts for the tier.

Determining the Short Option Minimum Charge: For each combined commodityin the portfolio:

-   -   For each directly calculated requirement level:        -   For each short option minimum rate tier            -   Determine the number of short option positions for the                tier.            -   Multiply by the short option minimum charge rate to                yield the charge for the tier.            -   Take the sum of the charges for the specific tiers,                yielding the overall charge for the combined commodity.

Aggregation of scaled-up risk array values to the scanning tier(s) andthe intercommodity spread tier(s): For each combined commodity in theportfolio for which scanning is being performed normally (not using the“liquidation risk” scanning method):

-   -   For each position in the combined commodity:        -   For each directly calculated requirement level for the            portfolio:            -   If intercurrency risk scanning is not enabled for the                product family for this position in this combined                commodity:                -   Increment each element in the overall scanning tier                    risk array, by the corresponding element in the                    scaled-up risk array for the position.                -   If there are specific scanning tiers for the                    combined commodity, select the specific scanning                    tier in which this product is contained, and                    increment each element in the risk array for the                    specific tier, by the corresponding element in the                    scaled-up risk array for the position.                -   Increment each element in the overall intercommodity                    spread tier risk array, by the corresponding element                    in the scaled-up risk array for the position.                -   If there are specific intercommodity spread tiers                    for the combined commodity, select the specific                    intercommodity spread tier in which this product is                    contained, and increment each element in the risk                    array for the specific tier, by the corresponding                    element in the scaled-up risk array for the                    position.            -   But if intercurrency risk scanning is enabled for the                product family for this position in this combined                commodity:                -   Increment each element in the overall scanning tier                    exchange rate up risk array for this settlement                    currency/performance bond currency pair, by the                    corresponding element in the scaled-up exchange rate                    up risk array for the position.                -   Increment each element in the overall scanning tier                    exchange rate down risk array for this settlement                    currency/performance bond currency pair, by the                    corresponding element in the scaled-up exchange rate                    down risk array for the position.                -   If there are specific scanning tiers for the                    combined commodity, select the specific scanning                    tier in which this product is contained, and:                -   Increment each element in the exchange rate up risk                    array for the specific tier for this settlement                    currency/performance bond currency pair, by the                    corresponding element in the scaled-up exchange rate                    up risk array for the position.                -   Increment each element in the exchange rate down                    risk array for the specific tier for this settlement                    currency/performance bond currency pair, by the                    corresponding element in the scaled-up exchange rate                    down risk array for the position.                -   Increment each element in the overall intercommodity                    spread tier exchange rate up risk array for this                    settlement currency/performance bond currency pair,                    by the corresponding element in the scaled-up                    exchange rate up risk array for the position.                -   Increment each element in the overall intercommodity                    spread tier exchange rate down risk array for this                    settlement currency/performance bond currency pair,                    by the corresponding element in the scaled-up                    exchange rate down risk array for the position.                -   If there are specific intercommodity spread tiers                    for the combined commodity, select the specific                    intercommodity spread tier in which this product is                    contained, and:                -   Increment each element in the exchange rate up risk                    array for the specific tier for this settlement                    currency/performance bond currency pair, by the                    corresponding element in the scaled-up exchange rate                    up risk array for the position.                -   Increment each element in the exchange rate down                    risk array for the specific tier for this settlement                    currency/performance bond currency pair, by the                    corresponding element in the scaled-up exchange rate                    down risk array for the position.

Aggregation of position delta to the delta periods: For each combinedcommodity in the portfolio for which scanning is being performednormally (not using the “liquidation risk” scanning method):

-   -   For each position in the combined commodity:        -   For each directly-calculated requirement level for the            combined commodity:            -   Take the position delta. (If the position is being                processed via split allocation, the position delta will                be zero and there is no need to continue.)            -   If the product is processed normally, increment the                period delta for this requirement level and for the                delta period containing this contract, by this position                delta.

If the product is processed using delta-split-allocation, allocate theposition deltas out to the underlying(s) Initialization of Tier Deltas

For intracommodity spread tiers:

-   -   For each combined commodity in the portfolio:        -   For each directly calculated requirement level:            -   For each intracommodity spread tier:                -   Initialize the total long delta for the specific                    tier by taking the sum of all period deltas                    contained within the tier which are positive (i.e.,                    net long.)                -   Initialize the total short delta for the specific                    tier by taking the sum of all period deltas                    contained within the tier which are negative (i.e.,                    net short), and then by taking the absolute value of                    this result.            -   For the overall tier:                -   Initialize the total long delta for the overall tier                    by taking the sum of the total long deltas for the                    specific tiers.                -   Initialize the total short delta for the overall                    tier by taking the sum of the total short deltas for                    the specific tiers.

For intercommodity spread tiers:

-   -   For each combined commodity in the portfolio:        -   For each directly calculated requirement level:            -   For each intercommodity spread tier:                -   Initialize the total long delta for the specific                    tier by taking the sum of all period deltas                    contained within the tier which are positive (i.e.,                    net long.)                -   Initialize the total short delta for the specific                    tier by taking the sum of all period deltas                    contained within the tier which are negative (i.e.,                    net short), and then by taking the absolute value of                    this result.                -   Net these two results against each other: subtract                    the total short delta from the total long delta. If                    the result is positive, store it as the total long                    delta and set the total short delta to zero. If the                    result is negative, take its absolute value, store                    it as the total short delta, and set the total long                    delta to zero.            -   For the overall tier:                -   Initialize the total long delta for the overall tier                    by taking the sum of the total long deltas for the                    specific tiers.                -   Initialize the total short delta for the overall                    tier by taking the sum of the total short deltas for                    the specific tiers.                -   Net these two results against each other: subtract                    the total short delta from the total long delta. If                    the result is positive, store it as the total long                    delta and set the total short delta to zero. If the                    result is negative, take its absolute value, store                    it as the total short delta, and set the total long                    delta to zero.

Determining the Scan Risk and Related Values for Scanning andIntercommodity Spreading Tiers: For each combined commodity in theportfolio for which scanning is being performed normally (not using the“liquidation risk” scanning method):

-   -   For the overall scanning tier, for the overall intercommodity        spreading tier, for each specific scanning tier if there are        any, and for each specific intercommodity spreading tier if        there are any:        -   For each directly calculated requirement level:            -   If intercurrency risk scanning was enabled for any                product family in this combined commodity:                -   For each settlement currency/performance bond                    currency pair for this combined commodity                    represented among the set of product families for                    which intercurrency risk scanning was enabled:                -   Compare each element in the exchange rate up array                    with the corresponding element in the exchange rate                    down array. For each element, select the larger                    value (more positive or less negative), thereby                    yielding the overall risk array for this tier and                    currency pair.                -   Sum the overall risk arrays for the various currency                    pairs for the tier, together with the array for the                    tier for products for which intercurrency risk                    scanning was not enabled (if any), thereby yielding                    the overall risk array for the tier.            -   Select the largest (most positive) value in the risk                array. This is the largest loss for the tier, and the                corresponding risk scenario is called the active                scenario. For scanning tiers only, this value is also                called the scan risk for the tier.            -   For intercommodity spread tiers only:                -   Select the risk array value with the same definition                    for price movement as the active scenario, but the                    opposite definition of volatility movement. This is                    called the paired point.                -   Take the average of the risk array values for the                    active scenario and the paired point. Round this                    result as specified in the rounding convention for                    time and volatility risks for this exchange complex,                    yielding an estimate of the volatility risk for the                    tier.                -   Take the two risk array values with scenario                    definitions of (a) no price change and (b) opposite                    volatility changes. Take the average of these two                    values, yielding an estimate of the time risk for                    the tier.                -   Subtract the estimates of volatility risk and time                    risk from the scan risk, yielding an estimate of the                    price risk.                -   Calculate the weighted price risk for the tier via                    one of three weighted price risk calculation                    methods.

Determining the weighted price risk for an intercommodity spread tier:There are three methods for calculating the weighted price risk for anintercommodity spread tier: normal, normal with capping, and scanrange.

If the method is normal:

-   -   Subtract the value of the short delta for the tier from the        value of the long delta for the tier, yielding the net delta for        the tier.    -   Divide the price risk for the tier by the net delta.    -   Take the absolute value of this result.

If the method is scanrange:

-   -   Select the first non-option contract within the tier that has a        non-zero value for its price scan range.    -   Take that price scan range.    -   Divide that value by the product of the contract's contract        scaling factor and delta-scaling factor. (This takes relative        contract size differences into account, converting the value        into one applicable to a “standard” sized contract.)

If the method is normal with capping:

-   -   Calculate the weighted price risk first via the normal method,        and again via the scanrange method.    -   Take the smaller of these two values. (In effect, it is        calculated normally, but its value is capped at the scan range.)

Determining the Scan Risk for the Combined Commodity: For each combinedcommodity within the portfolio for which scanning is being performednormally (not using the “liquidation risk” scanning method):

-   -   For each directly calculated requirement level for that combined        commodity:        -   If there are any specific scanning tiers defined for the            combined commodity:            -   The scan risk for the combined commodity is the sum of                the tier scan risks for each specific scanning tier.        -   But if there is only the overall scanning tier for the            combined commodity:            -   The scan risk for the combined commodity is the scan                risk for that overall scanning tier.

Determining the Scan Risk and setting other values for the CombinedCommodity using the Liquidation Risk Method: Each combined commodity forwhich Liquidation Risk has been specified as the processing method forscanning will contain only physical equity or debt securities which areconsidered to (a) be within the same security family and (b) have thesame risk level.

Each such combined commodity will have only overall tiers defined for itfor scanning, for intercommodity spreading, and for intracommodityspreading.

Each such combined commodity will have precisely one intracommodityspread defined for it, a delta-based, one to one, overall tier 1 tooverall tier 1 spread. The charge rate for this spread will be specifiedas a decimal fraction. Intercommodity spreads referencing this combinedcommodity will similarly reference the overall intercommodity spreadtier, with a credit rate specified as a decimal fraction.

For each combined commodity for which Liquidation Risk has beenspecified as the method for determining the Scan Risk:

-   -   Take the sum of the Liquidation Risk Position Values for all        positions for which this value is positive. This yields the Long        Liquidation Value.    -   Take the sum of the Liquidation Risk Position Values for all        positions for which this value is negative. Then take the        absolute value of this sum. This yields the Short Liquidation        Value.    -   For each directly-calculated requirement level for this combined        commodity:        -   Read the Liquidation Risk rates for this requirement level            and combined commodity. There will be two values, the            Specific Rate and the Generic Rate. (These are also referred            to as the X-parameter and the Y-parameter, respectively, in            the Paris Bourse documentation.)        -   Take the sum of the Long Liquidation Value and the Short            Liquidation Value, and multiply this result by the Specific            Rate. This yields the Specific Risk.        -   Take the absolute value of the difference between the Long            Liquidation Value and the Short Liquidation Value, and            multiply this result by the Generic Rate. This yields the            Generic Risk.        -   Take the sum of the Specific Risk and the Generic Risk.        -   Store the Long Liquidation Value as the Long Delta for the            overall Intracommodity Spread Tier.        -   Store the Short Liquidation Value as the Short Delta for the            overall Intracommodity Spread Tier.        -   Subtract the Short Liquidation Value from the Long            Liquidation Value. If this result is zero or positive, store            it as the Long Delta for the overall Intercommodity Spread            Tier. If this result is negative, take its absolute value            and store it as the Short Delta for the overall            intercommodity spread tier.        -   Set the Weighted Price Risk for the overall intercommodity            spread tier to 1.

Spreading: After determining the scan risk and the minimum commoditycharge for each combined commodity in the portfolio, the next step is toperform spreading. As will be described below, the disclosed embodimentsutilize the following spreading and hybrid spreading methodologies.

Spread groups: The SPAN algorithm supports the definition of thefollowing groups of spreads:

-   -   Super-intercommodity spreads    -   Intra-commodity spreads    -   Pre-crossmargining spreads    -   Cross-margining spreads    -   Inter-commodity spreads    -   Inter-clearing organization (“interexchange”) spreads

Intra-commodity spreads and inter-commodity spreads are the mostfamiliar types.

Intra-commodity spreads are typically used to calculate charges torecognize the risk associated with spreads formed within a combinedcommodity. These can be needed since the scanning process assumesperfect correlation of price movements among the various productsgrouped together within a combined commodity.

Inter-commodity spreads are used to recognize risk offsets, and provideappropriate credits, between positions in related combined commodities.

Inter-clearing organization spreads, often referred to as interexchangespreads, are used to recognize risk offsets and provide appropriatecredits, between positions in combined commodities of different clearingorganizations or other business functions of those clearingorganizations. These are distinguished from normal intercommodityspreads in that each clearing organization involved in a particularspread is free to recognize or not recognize that spread, and to specifythe particular credit rate applicable to its own products. This may beused when a clearing organization wishes to grant a reduction to theperformance bond requirement for its own products when the risk of thoseproducts is reduced by offsetting positions on another clearingorganization, regardless of whether any formal cross-margining agreementexists between those clearing organizations, and typically in theabsence of any such agreement.

Super-intercommodity spreads are a new spread group created in order toallow the recognition of particular delta patterns across combinedcommodities, even before intracommodity spreading is performed. Forexample, this type of spread can be used to recognize a “tandem”relationship between two combined commodities (for the first combinedcommodity: long in one month, short in another; and for the secondcombined commodity: short in one month, long in another.)

Cross-margining spreads are a new group created in order to allow two ormore clearing organizations which participate in a cross-marginagreement, to define spreads which are to be evaluated before normalintra- and inter-commodity spreading is done. The newpre-cross-margining spread group gives those same clearing organizationsan opportunity to define spreads which are to be evaluated first, beforethe cross-margining spreading is done.

Spread types: In addition to the spread group in which they arecontained, spreads may be categorized by whether they are delta-based,scanning-based, or hybrid delta-based/scanning-based.

Scanning-based spreads and hybrid spreads can only be used for theintercommodity spread groups—pre-crossmargin spreads,super-intercommodity spreads, and normal intercommodity spreads.

Spreads in the groups that cross clearing organization and/or businessfunction boundaries—the crossmargining spreads and the inter-clearingorganization spreads—can only be delta-based.

Delta-Based Spreading: A delta-based spread is one that is formed on adelta-basis—i.e., according to the relative magnitudes and relationshipsof the remaining delta values for each of the legs of the spread.

A delta-based spread may contain any number of spread legs. Spreads aretypically two-legged, but three, four, five or more legged-spreads mayoccur.

Each leg references a specific combined commodity, and for that combinedcommodity, one of:

-   -   an intercommodity spread tier    -   an intracommodity spread tier, or    -   a delta period.

In addition, for each leg, a delta per spread ratio and a relativemarket side indicator are specified.

The delta per spread ratio is a positive value, which indicates theamount of delta consumed for that leg via the formation of one spread.

The relative market side indicator is either A or B, and indicates therelative relationship of the remaining deltas of the legs which mustprevail in order for spreads to be formed. For example, for a typicaltwo-legged A to B spread, either the remaining delta for the first legmust be positive and the second leg negative, or the remaining delta forthe first leg must be negative and the second leg positive.

A delta-based spread also has defined for it a charge or creditmethod—either flat-rate, or weighted price risk:

-   -   Flat-rate is typically used for intracommodity spreads. A charge        for the spread is calculated by taking the number of spreads        formed and multiplying by the charge rate.    -   Weighted price risk is typically used for intercommodity        spreads. For each participating leg, a credit for the spread is        calculated by determining the total number of delta consumed by        the spread, times the weighted price risk (which can be thought        of as the price risk per delta), times the credit rate        percentage.

Accordingly, a delta-based spread also has defined for it one or morerates, depending on how many requirement levels are being directlycalculated.

For an intracommodity spread using the flat-rate method, the rates areconsidered to be charge rates, and a normal, positive charge rateproduces an intracommodity spread charge. A negative charge rate isallowed and would produce a negative charge—i.e., a credit.

Similarly, for an intercommodity spread using the weighted price riskmethod, a normal, positive credit rate percentage produces a positivecredit amount. If a negative credit rate had been specified for thespread, this would yield a negative credit—i.e., a charge.

Delta-based spreads using the flat rate method may have more than onecombined commodity represented among their legs. If so, the resultingcharge is apportioned to each leg according to the relative proportionof the absolute value of its delta per spread ratio. All such combinedcommodities participating in such a spread must accordingly share thesame performance bond currency.

Spreads within spreads: Sometimes it may be desired to use onedelta-based spread to set a limit on the total number of spreads formedvia a separate set of delta-based spreads.

To handle these situations generically, delta-based spreads have beenmade recursive in SPAN.

That is, a delta-based spread may contain a set (one or more) ofdelta-based spreads, each of which may contain a set (one or more) ofdelta-based spreads. There are no limits to the numbers of levels ofsuch recursions.

The spread at the top of such a hierarchy is called the top-levelspread, and it is the one that contains the rate(s) for the spread.Spreads at lower levels do not have rates defined for them.

The basic idea here is that each spread sets an upper bound on thenumber of spreads which can be formed by spreads contained within it. Inthe typical case, there is only one level of recursion, with a top-levelspread containing a set of child spreads, each of which does not havechildren. In this case, the top-level spread sets an overall upper boundon the number of spreads formable by its child spreads.

Creating the combined pools of inter-clearing organization spreads andof crossmargining spreads

Except for spreads in the crossmargining group and the inter-clearingorganization group, spreads in each group are evaluated exchange complexby exchange complex, and it does not matter in which order the exchangecomplexes are processed.

For the crossmargining group and the inter-clearing organization group,however, processing is not done by exchange complex. Instead, singlepools of spreads are created which include all spreads provided for anyexchange complex represented in the portfolio. This process has severalimportant characteristics:

-   -   Duplicate spreads are recognized: suppose, for example, that        clearing organization X recognizes a 1 to 1, A to B spread for        one of its products against a related product on clearing        organization Y. Suppose further that clearing organization Y        recognizes the same spread against clearing organization X.    -   In this case, the algorithm must recognize that these are the        same spread.    -   Each clearing organization can only provide a credit for its own        products. In this example, when clearing organization X        specifies the spread, the credit rate(s) it specifies only apply        to its own products. And similarly for clearing organization Y.    -   If clearing organization X recognizes the spread while        organization Y does not, then the credit rate specified by X        will apply only to X's products. Y's products will have a credit        rate of zero.    -   If both organizations recognize the spread, there nevertheless        is no guarantee that they will have the same credit rates. X may        specify one rate applicable to its products, and Y may specify a        different rate applicable to its products.    -   Spreads are prioritized by greatest total savings. The spreads        in the combined pool must be prioritized according to greatest        total savings across all legs.

Evaluating spreads group by group: For each exchange complex in theportfolio:

-   -   For the spreads in the super-intercommodity spread group:        -   Evaluate each spread within the group in turn, in order by            spread priority.

For each exchange complex in the portfolio:

-   -   For the spreads in the intracommodity spread group:        -   Evaluate each spread within the group in turn, in order by            spread priority.

Finalize the spot charges for all delta periods to which they apply.

For each exchange complex in the portfolio:

-   -   For the spreads in the pre-crossmargining spread group:        -   Evaluate each spread within the group in turn, in order by            spread priority.

For the combined pool of crossmargining spreads:

-   -   Evaluate each spread in the pool, ordered as described above in        descending order by total savings.

For each exchange complex in the portfolio:

-   -   For the spreads in the intercommodity spread group:        -   Evaluate each spread within the group in turn, in order by            spread priority.

For the combined pool of inter-clearing organization spreads:

-   -   Evaluate each spread in the pool, ordered as described above in        descending order by total savings.

Evaluating a delta-based spread—Overview: The overall process forevaluating a delta-based spread that has no child spreads can besummarized as follows:

First, check to make sure that each of the spread legs is present in theportfolio.

Then attempt to form spreads under each of the two possible assumptionsof market side. In other words, first attempt to form spreads assumingthat the “A” legs are long and the “B” legs are short. Then reverse theassumption and attempt to form spreads assuming that the “A” legs areshort and the “B” legs are long.

Under either assumption, if any spreads can be formed, determine foreach leg the delta consumed by the spread. Remove the consumed deltafrom the remaining delta for that spread leg. Then re-evaluate deltavalues as needed so that remaining period deltas, intracommodity spreadtier deltas, and intercommodity spread tier deltas are keptsynchronized.

Last, determine the charge or credit associated with the spreads formed.

Determining the delta consumed for a particular leg of a delta-basedspread under a particular assumption of market side:

-   -   Take the number of spreads formed.    -   Multiply by the delta per spread ratio for the leg.    -   If the current assumption is that the A side is long and this is        a B leg, OR if the current assumption is that the A side is        short and this is an leg, then multiply the above result by −1        to make it negative. (In other words, in this case, short delta        has been consumed.)

Removing the delta consumed for a particular leg of a delta-based spreadunder a particular assumption of market side:

-   -   Initialize the remaining delta to be removed, as the delta to be        consumed.    -   If the leg references a spread tier—either an intracommodity or        an intercommodity spread tier, and either a specific tier or the        overall tier:        -   Beginning with the first delta period within the tier and            continuing with each subsequent delta period within the            tier, remove delta from each such period sequentially until            remaining delta to be removed is zero.    -   But if the leg references a specific delta period, then remove        delta from that specific period.    -   For each intracommodity or intercommodity spread tier containing        the period from which some delta was removed decrement remaining        long or short delta by the amount of delta removed from the        period.

Calculating the credit for a particular leg of a delta-based spreadwhich uses the weighted price risk method, and incrementing the creditamount for the appropriate tier: This would be for a delta-based spreadthat uses the weighted price risk method. Each leg of such a spreadwould reference either an intercommodity spread tier or a delta periodfor a combined commodity. If the leg references a tier, it will beeither the overall intercommodity spread tier or, if specific tiers aredefined, a specific intercommodity spread tier.

-   -   Take the absolute value of the delta consumed by the spread for        this leg.    -   Determine the tier to use for reading the weighted price risk:        -   If the leg references an intercommodity spread tier, select            that tier.        -   If the leg references a delta period:            -   If specific intercommodity spread tiers are defined,                select the specific tier containing this period.            -   If no specific tiers are defined, select the overall                intercommodity spread tier.    -   Take the absolute value of the delta consumed by the spread for        this leg and this requirement level.    -   Multiply this result by the weighted price risk for the selected        tier and this requirement level.    -   Multiply this result by the credit rate for the spread for this        leg and this requirement level.    -   If the spread giving rise to this credit is in any spread group        other than the cross-margin spread group or the inter-clearing        organization spread group:        -   Increment the intercommodity spread credit for the selected            tier, by the credit for this leg for this spread.    -   But if the spread giving rise to this credit is in either the        cross-margin spread group or the inter-clearing organization        spread group:        -   Increment the inter-clearing organization spread credit for            the selected tier, by the credit for this leg for this            spread.            (As described above, if the credit rate were negative, this            would yield a negative credit—i.e., a charge.)

Calculating the charge for a delta-based spread which uses the flat-ratemethod: This could apply to a pre-crossmargining spread, asuper-intercommodity spread, an intracommodity spread, or anintercommodity spread.

-   -   Take the number of spreads formed.    -   Multiply by the charge rate for the spread for this requirement        level.

Scanning-Based Spreads: Scanning-based spreads are inherentlyintercommodity spreads, and can only be present within the three spreadgroups which (a) include more than one combined commodity among the legsand (b) do not cross exchange complexes. These groups are:pre-crossmargin spreads, super-intercommodity spreads, and normalintercommodity spreads.

A scanning-based spread is similar to a delta-based spread in that itcontains a collection of legs. Each leg, however, references only aspecific combined commodity.

The relative market side indicator is not applicable to the legs of ascanning-based spread. The delta per spread ratio is applicable, but, aswill be described below, its application is somewhat different for ascanning-based spread than for a delta-based spread.

One of the legs of a scanning-based spread is designated as the targetleg, and there is an associated parameter of the target leg called thetarget leg required flag:

-   -   If the target leg required flag is true, then the combined        commodity designated as the target leg must be present in the        portfolio in order for the spread to be formed, and if it is        not, the spread is skipped.    -   If the target leg required flag is false, then the combined        commodity designated as the target leg need not be present in        the portfolio in order for the spread to be formed.

Similarly, for each leg which is not the target (a “non-target leg”),there is a parameter called the leg-required flag. If any non-target legwhich is specified as required is not present in the portfolio, then thespread is skipped. In other words, all required non-target legs must bepresent in the portfolio in order for the spread to be formed.

As with a delta-based spread, a scanning-based spread has one or morecredit rates specified for it, for different account types andrequirement levels for those account types.

All legs for a scanning-based spread must have the same scan pointdefinitions.

Evaluating a Scanning-Based Spread: Verify that all of the required legsare represented in the portfolio. Skip the spread if not.

-   -   For the target leg:        -   Aggregate from the target leg and each of the non-target            legs, thereby yielding the new value for the target leg,            each of the eight types of position value, converted as            needed to the performance bond currency of the target leg.    -   For each directly calculated requirement level:        -   For each scanning tier for the target leg:            -   For the target leg and for each non-target leg:                -   Perform the Risk Array Scaling and Currency                    Conversion Algorithm:                -   Take the risk array for the tier.                -   For each value in the risk array:                -   If this value is negative (i.e., a gain), multiply                    it by the credit rate expressed as a decimal                    fraction.                -   If this leg is not the target, and if the                    performance bond currency for this leg is different                    from the performance bond currency for the target                    leg, then convert the value to the performance bond                    currency of the target.            -   Take the sum all of these appropriately scaled and                converted risk arrays. This yields the new risk array                for the overall scanning tier for the target leg.            -   Select the largest loss and determine the scan risk and                active scenario, exactly as for any scanning tier.            -   For each non-target leg:                -   Set each value in the risk array for the tier to                    zero.                -   Then repeat the process of selecting the largest                    loss and determining the scan risk, thereby setting                    these values to zero.        -   For each delta period for the target leg:            -   For the corresponding delta period for each non-target                leg that exists:                -   Divide the delta-per-spread ratio for the target leg                    by the delta-per-spread ratio for this non-target                    leg, yielding the aggregation ratio:                -   Determine the remaining delta to be aggregated:                -   Multiply the remaining delta for this delta period                    by the aggregation ratio.                -   Determine the original delta to be aggregated:                -   Multiply the original delta for this delta period by                    the aggregation ratio.            -   Take the sum of the remaining delta to be aggregated                values from the corresponding delta period for each                non-target leg that exists, and add this result to the                remaining delta for this delta period on the target leg,                yielding the new value for remaining delta for the                target leg.            -   Take the sum of the original delta to be aggregated                values from the corresponding delta period for each                non-target leg that exists, and add this result to the                original delta for this delta period on the target leg,                yielding the new value for original delta for the target                leg.            -   Take the sum of the Delivery (Spot) Charge for Delta                Consumed by Spreads from the corresponding delta period                for each non-target leg that exists (converted as needed                to the performance bond currency of the target leg), and                add this result to the same value on the target leg,                yielding the new value for Delivery (Spot) Charge for                Delta Consumed by Spreads for this delta period for the                target leg.            -   Take the sum of the Delivery (Spot) Charge for Delta                Remaining in Outrights from the corresponding delta                period for each non-target leg that exists (converted as                needed to the performance bond currency of the target                leg), and add this result to the same value on the                target leg, yielding the new value for Delivery (Spot)                Charge for Delta Remaining in Outrights for this delta                period for the target leg.            -   Set to zero for the corresponding delta period for each                non-target leg:                -   Original delta and remaining delta                -   Delivery charge for delta consumed by spreads, and                    delivery charge for delta remaining in outrights        -   For each intercommodity spread tier for the target leg:            -   For the target leg and for each non-target leg:                -   Perform the same Risk Array Scaling and Currency                    Conversion Algorithm as described above for the                    scanning tiers            -   Take the sum all of these appropriately scaled and                converted risk arrays. This yields the new risk array                for the intercommodity spread tier for the target leg.            -   Aggregate from the target leg and each non-target leg,                thereby yielding the new value for the target leg, each                of the following elements:                -   Intercommodity spread credit (converted as needed to                    the performance bond currency of the target leg)                -   Inter-clearing organization spread credit (converted                    as needed to the performance bond currency of the                    target leg)            -   Take the sum of the original delta for each delta period                within this tier which is positive, yielding the new                value for original long delta for the tier.            -   Take the sum of the remaining delta for each delta                period within this tier which is positive, yielding the                new value for remaining long delta for the tier.            -   Take the sum of the original delta for each delta period                within this tier which is negative, yielding the new                value for original short delta for the tier.            -   Take the sum of the remaining delta for each delta                period within this tier which is negative, yielding the                new value for remaining short delta for the tier.            -   Select the largest loss and determine the time risk,                volatility risk, price risk and weighted price risk,                exactly as for any intercommodity spreading tier.            -   For each intercommodity spread tier for each non-target                leg:                -   Set each value in the risk array for the tier to                    zero.                -   Set the original delta and remaining delta values to                    zero.                -   Set the intercommodity spread credit and                    inter-clearing organization spread credit to zero.                -   Repeat the process of determining the largest loss,                    volatility risk, time risk, price risk and weighted                    price risk, thereby setting all of these values to                    zero.        -   For each intracommodity spread tier for the target leg:            -   Take the sum of the original delta for each delta period                within this tier which is positive, yielding the new                value for original long delta for the tier.            -   Take the sum of the remaining delta for each delta                period within this tier which is positive, yielding the                new value for remaining long delta for the tier.            -   Take the sum of the original delta for each delta period                within this tier which is negative, yielding the new                value for original short delta for the tier.            -   Take the sum of the remaining delta for each delta                period within this tier which is negative, yielding the                new value for remaining short delta for the tier.            -   For each intracommodity spread tier for each non-target                leg:                -   Set the original delta and remaining delta values to                    zero.        -   For each short option minimum tier for the target leg:            -   Aggregate from the target leg and the equivalent tier on                each non-target leg, thereby yielding the new for the                target leg, each of the following elements:                -   Number of short puts                -   Number of short calls                -   Short option minimum charge (converted as needed to                    the performance bond currency for the target leg)            -   For each non-target leg:                -   Set the number of short puts, the number of short                    calls, and the short option minimum charge, to zero.        -   For the target leg combined commodity for this requirement            level:            -   Aggregate from the target leg and each non-target leg,                thereby yielding the new value for the target leg:                -   Intracommodity spread charge (converted as needed to                    the performance bond currency of the target leg)

Hybrid Delta-Based/Scanning-Based Spreads: A hybriddelta-based/scanning-based intercommodity spread combines elements ofdelta-based spreading and scanning-based spreading.

Hybrid spreads may be present only in the normal intercommodity spreadgroup, or the pre-crossmargining spread group.

Like a regular delta-based spread, the delta-based spread part of thehybrid spread definition will contain a collection of delta-based spreadlegs. There are several restrictions, however, on the specification ofthe spread and of its spread legs:

-   -   The spread is not recursive—i.e., it may not contain a        subsidiary collection of delta-based spreads.    -   Each spread leg may reference only the overall intercommodity        spread tier of a specific combined commodity. References to        specific intercommodity spread tiers or to delta periods are not        allowed.    -   All of the combined commodities referenced as legs of the        delta-based spread must have the same performance bond currency.    -   A charge rate must be specified for the delta-based spread,        which rate is denominated in that same performance bond        currency.

Like a scanning-based spread, a hybrid spread will also specify a targetleg, which will reference a specific combined commodity. This targetcombined commodity is never one into which any products are linked. Itis not referenced by any spread until the hybrid spread for which it isspecified as the target. After this spread, it may subsequentlyparticipate in intercommodity spreading, but only as a leg of a regulardelta-based spread.

Here's the detailed algorithm for evaluating a hybrid spread:

-   -   For each directly-calculated requirement level:        -   Perform the Algorithm for evaluating a top-level delta-based            spread as described above, with one exception as specified            herein:            -   This has the effect of determining under each assumption                of relative market-side, the number of delta-based                spreads formable, of calculating the associated charge,                and of decreasing series and tier deltas for each leg                according to the delta consumed by the spread.            -   The exception is that the charge calculated under each                assumption of relative market-side is not apportioned                back to the legs of the spread. Instead, the charges                calculated under each assumption are summed to yield the                basis risk.        -   Take the sum of the scan risk values for each of the overall            intercommodity spread tiers in the non-target legs            participating in the spread, yielding the total scan risk.        -   Now perform the Algorithm for evaluating a scanning-based            spread as described above, using a 100% credit rate, but            with the following exceptions:            -   For each non-target leg, for the overall scanning tier,                for any specific scanning tiers, for the overall                intercommodity spreading tier, and for any specific                intercommodity spreading tiers, do not set each value in                the risk array for the tier to zero, and do not then                re-evaluate for the tier the scan risk and (for the                intercommodity spread tiers) the time risk, volatility                risk, price risk and weighted price risk.            -   Similarly, do not aggregate from the non-target legs to                the target leg, and then set to zero on the non-target                legs: the intracommodity spread charge                -   for the overall intercommodity spread tier and for                    any specific intercommodity spread tiers, the                    intercommodity spread credit and the inter-clearing                    organization spread credit                -   for each delta period, the charge for delta consumed                    by spreads and the charge for delta remaining in                    outrights                -   for the overall short option minimum rate tier and                    for any specific short option minimum rate tiers,                    the short option minimum charge, and the number of                    short puts and the number of short calls            -   For the target leg, after determining the weighted price                risk:                -   Save the value for the scan risk on the target leg                    as the scan together risk.                -   For the overall intercommodity spread tier, the                    overall scan tier, and any specific intercommodity                    spread tiers and specific scanning tiers:                -   set the scan risk value to zero                -   for the intercommodity spread tiers, set the time                    risk, volatility risk, and price risk to zero,                    leaving only the value for weighted price risk.            -   The net result of this processing is that:                -   Remaining deltas have been aggregated for                    intracommodity spread tiers, intercommodity spread                    tiers, and delta periods, from the non-target legs                    to the target.                -   Weighted price risk has been determined for the                    overall intercommodity spread tier on the target.                -   All other elements of the SPAN risk calculation                    remain with the non-target legs: the scan risk,                    intracommodity spread charge, short option minimum,                    spot charge, intercommodity spread credit, and                    inter-clearing organization spread credit.                -   The value that would have been the scan risk for the                    target leg in a normal scanning-based spread has                    been saved as the scan together risk.        -   Take the sum of basis risk and scan together risk. Subtract            this sum from the total scan risk. Divide this result by            total scan risk. Take the larger of this result, and zero,            thereby yielding the savings percentage.        -   For the overall intercommodity spread tier for each            non-target leg:            -   Take the largest loss for the tier.            -   Multiply by the savings percentage, yielding the credit                for this leg for the spread.            -   Round this result to the normal precision for values                denominated in this currency.            -   Increment the intercommodity spread credit for the tier,                by this amount.            -   Again take the largest loss for the tier. Divide this                value by the scan together risk. Save this result as the                scan risk percentage for subsequent use.

Execution now proceeds to the next spread definition in the spreadgroup, and to the remaining spread groups to be evaluated.

As it does, the overall intercommodity spread tier of the combinedcommodity, which was the target of the original hybrid spread, mayparticipate as a leg of other delta-based intercommodity spreads usingthe weighted price risk method of determining the credit.

If this occurs, the intercommodity spread credit for the original targetleg calculated as a result of that delta-based spread, is apportionedback to the original non-target legs of the original hybrid spread, inproportion to the scan risk for that leg to the total scan risk. Here'show:

-   -   For each directly-calculated requirement level for the original        hybrid spread target leg:        -   Take the intercommodity spread credit value just calculated.        -   For each original non-target leg for the original hybrid            spread:            -   Multiply the above value by the scan risk percentage for                that non-target leg.            -   Round this result to the normal precision for the                performance bond currency for that non-target leg.            -   Increment the intercommodity spread credit (or the                inter-clearing organization spread credit if the spread                now being processed is within the inter-clearing                organization spread group or the cross-margin spread                group) by this result.        -   Set the intercommodity spread value for the original hybrid            spread target leg back to zero.

Finalizing the Spot Charge: This calculation will be performed for eachcombined commodity, after all spreads in the intracommodity spread grouphave been evaluated, but before any of the subsequent spread groups havebeen processed.

-   -   For each combined commodity in the portfolio:        -   For each directly calculated requirement level for this            combined commodity:            -   For each delta period for this combined commodity to                which spot charges apply:                -   If for this delta period it has been specified that                    spot charges apply to either long or short delta, OR                    if it has been specified that they apply to long                    delta only and the remaining delta for the period is                    positive, OR if it has been specified that they                    apply to short delta only and the remaining delta                    for the period is negative:                -   Subtract the remaining delta for this period and                    requirement level from the original value for delta                    for the period and this requirement level. Take the                    absolute value of this amount. This yields the delta                    consumed by spreads.                -   Take the absolute value of the remaining delta for                    this period. This yields the delta remaining in                    outrights.                -   Multiply the delta consumed by spreads, by the                    charge rate for delta consumed by spreads, yielding                    the spot charge for delta consumed by spreads for                    this period and requirement level.                -   Multiply the delta remaining in outrights, by the                    charge rate for delta remaining in outrights,                    yielding the spot charge for delta remaining in                    outrights for this period and requirement level.                -   Otherwise, the values for these two charges are                    zero.            -   Sum the spot charge for delta consumed by spreads for                each period, yielding the total spot charge for delta                consumed by spreads for this combined commodity for this                requirement level.            -   Sum the spot charge for delta remaining in outrights for                each period, yielding the total spot charge for delta                remaining in outrights for this combined commodity for                this requirement level.            -   Sum the spot charge for delta consumed by spreads, and                the spot charge for delta remaining in outrights,                yielding the total spot charge for the combined                commodity and this requirement level.

Finalizing the Intercommodity Spread Credit and the Interexchange SpreadCredit: For each combined commodity in the portfolio:

-   -   For each directly calculated requirement level for the combined        commodity:        -   Take the sum of the intercommodity spread credit for the            overall intercommodity spread tier, and the intercommodity            spread credits for each specific intercommodity spread tier,            if any. This yields the total intercommodity spread credit            for the combined commodity.        -   Take the sum of the inter-clearing organization spread            credit for the overall intercommodity spread tier, and the            inter-clearing organization spread credits for each specific            intercommodity spread tier, if any. This yields the total            inter-clearing organization spread credit for the combined            commodity.

Finalizing the SPAN Requirement(s) for Directly Calculated RequirementLevels For each combined commodity in the portfolio:

-   -   For each directly calculated requirement level for the combined        commodity:        -   Take the sum of the scan risk, the intracommodity charge,            and the spot charge. (This value is sometimes called the            commodity risk.)        -   Subtract from this value, the sum of the intercommodity            spread credit and the inter-clearing organization spread            credit. (This value is sometimes called the prototype SPAN            risk, or the pre-SPAN risk.)        -   Take the larger of this value and the short option minimum.        -   If a risk adjustment factor is defined for this directly            calculated requirement level, multiply the above result by            this risk adjustment factor.        -   If the positions in this combined commodity consist solely            of long positions in option products, all of which options            have non-zero values for their prices, then take the smaller            of this result and the current value of those options in the            performance bond currency.        -   The result is the SPAN risk requirement for this requirement            level.

The third to last step is called capping the risk at long option valuefor portfolios consisting solely of long options. Note that the value atwhich the risk is capped may include both futures-style options andpremium-style options. The key factor here is not how the options arevalued, but whether they are long positions in products for which thecurrent value of the risk is limited to the current value of thepositions themselves.

Determining Derived SPAN risk requirements: For each combined commodityrepresented in the portfolio:

-   -   For each directly calculated requirement level for this combined        commodity:        -   For each risk adjustment factor applicable to that            requirement level or to any requirement level derived from            that requirement level:            -   Process each such risk adjustment factor in turn:                -   Take the SPAN risk requirement for the base                    requirement level.                -   Multiply by the risk adjustment factor, which                    converts a requirement from the specified base                    requirement level to the specified derived                    requirement level.                -   If the positions in this combined commodity consist                    solely of long positions in option products, all of                    which options have non-zero values for their prices,                    then take the smaller of this result and the current                    value of those options in the performance bond                    currency.                -   The result is the SPAN risk requirement for the                    derived requirement level.

Typically risk adjustment factors used to determine derivedrequirements, are used to determine an initial requirement level from amaintenance requirement level.

Determining the Available Net Option Value: For each combined commodityin the portfolio:

-   -   Determine the total net value in the performance bond currency        of all positions in the portfolio for this combined commodity        which are valued premium-style, as follows:        -   Take the following four values denominated in the            performance bond currency:            -   value of long option positions in products valued                premium-style            -   value of short option positions in products valued                premium-style            -   value of long non-option positions in products valued                premium-style            -   value of short non-option positions in products valued                premium-style        -   If there are any portion of these position values for which            full credit is not being given due the premium not yet            having been paid or collected, adjust these values            accordingly to remove that portion.        -   Subtract the adjusted value of short option positions valued            premium-style from the adjusted value of long option            positions valued premium-style, yielding the net value of            option positions valued premium-style.        -   Subtract the adjusted value of short non-option positions            valued premium-style from the adjusted value of long            non-option positions valued premium-style, yielding the net            value of non-option positions valued premium-style.        -   Take the sum of these two net values, yielding the net            adjusted value of positions valued premium-style.    -   For each requirement level for this combined commodity (whether        directly calculated or derived):        -   If for this combined commodity capping off available net            option value at the risk has been enabled, then take the            smaller of the net adjusted value of positions valued            premium-style, and the SPAN risk requirement, yielding the            available net option value for this requirement level.        -   But if such capping has not been enabled, the available net            option value for this requirement level is equal to the net            adjusted value of positions valued premium-style.

The SPAN calculation for omnibus accounts and other gross-marginedfirm-level accounts: As described above in the introductory section,Portfolios to be margined, an omnibus account is:

-   -   a firm-level account type    -   for which total positions are maintained on a gross basis—i.e.,        they may be simultaneously long and short    -   for which subaccounts may be defined    -   for which the portion of the total long and total short        positions which are not contained in said defined subaccounts,        are considered to be the naked long and naked short positions    -   for which the naked long and naked short positions are margined        on a gross basis—in other words, treated as if each such naked        long position and each such naked short position is in a        portfolio by itself, without any risk reductions due to        offsetting positions.

Generically, a gross-margined firm-level account is any such account forwhich naked long and naked short positions are margined in this manner.An omnibus account may be considered to be an example of such an accountfor which there may also be positions in defined subaccounts.

This section describes the overall process for determining the SPAN riskrequirements and the Available Net Option Values for the combinedcommodities represented in the portfolio for gross-margined firm-levelaccounts. This process consists of:

-   -   Determining the naked long and naked short positions    -   Calculating SPAN requirements for the subaccounts, if any    -   Calculating SPAN requirements for the naked positions    -   Aggregating SPAN requirements for the subaccounts with the SPAN        requirements for the naked positions, in order to determine the        total SPAN requirement values for the combined commodity.

Determining the Naked Positions: For each position in the omnibusaccount:

-   -   Take the sum of all subaccount positions in this product that        are net long.    -   Subtract this result from the Total Long position quantity for        the omnibus account, yielding the Naked Long position.    -   Take the absolute value of the sum of all subaccount positions        in this product that are net short.    -   Subtract this result from the Total Short position quantity for        the omnibus account, yielding the Naked Short position.

Note that for each product represented in the omnibus account portfolio,the Total Long position must be at least as great as the sum of thesubaccount positions that are net long, and the Total Short positionmust be at least as great as the absolute value of the sum of thesubaccount positions that are net short. Naked position quantities maybe zero, but by definition they may never be negative.

Calculating SPAN requirements for subaccounts: Whenever the SPANcalculation is to be performed for an omnibus account, after determiningthe naked positions, the normal SPAN calculation for net portfoliosshould be performed for each subaccount of that omnibus account, if anyare defined.

For each such subaccount, for each combined commodity represented in theportfolio for the subaccount, the result will be the SPAN riskrequirement and Available Net Option Value for each directly-calculatedand indirectly-calculated requirement level for that combined commodity.

Evaluating the SPAN requirements for the subaccounts first simplifiesthe SPAN calculation for the omnibus account, in that it ensures thatthe subaccount requirements will be available for aggregation to theomnibus account when they are needed.

Calculating SPAN requirements for naked positions: For each combinedcommodity in the portfolio:

-   -   For each position for this combined commodity:        -   For the naked long position quantity, perform the Naked            Position SPAN evaluation algorithm to determine for each            directly and indirectly calculated requirement level for            this combined commodity:            -   the SPAN risk requirement            -   the Available Net Option Value        -   For the naked short position quantity, perform the Naked            Position SPAN evaluation algorithm to determine for each            directly and indirectly calculated requirement level for            this combined commodity:            -   the SPAN risk requirement            -   the Available Net Option Value        -   For each directly and indirectly calculated requirement            level for this combined commodity:            -   Sum the SPAN requirement for naked longs for this                requirement level, and the SPAN requirement for naked                shorts for this requirement level, yielding the total                SPAN requirement for nakeds for this position and this                requirement level.            -   Sum the Available Net Option Value for naked longs for                this requirement level, and the Available Net Option                Value for naked shorts for this requirement level,                yielding the total Available Net Option Value for nakeds                for this position and this requirement level.    -   For each directly and indirectly calculated requirement level:        -   Take the sum of the SPAN requirement for nakeds, across all            positions for the combined commodity, yielding the SPAN            requirement for naked positions for the combined commodity            for this requirement level.        -   Take the sum of the Available Net Option Value for nakeds,            across all positions for the combined commodity, yielding            the Available Net Option Value for naked positions for the            combined commodity for this requirement level.

Naked Position SPAN Evaluation Algorithm: As described above, thisalgorithm is described to either the naked long quantity or the nakedshort quantity of a position held in a gross-margined account, either atthe firm-level or the clearing-level.

-   -   Create a net portfolio for the purpose of this calculation,        consisting solely of this naked long (or naked short) position.    -   Apply the SPAN algorithm to this net portfolio.    -   For each requirement level directly calculated:        -   Determine the SPAN requirement and the Available Net Option            Value for this requirement level and for the combined            commodity containing the net position.        -   If split allocation or margining-positions-as-equivalents            caused other combined commodities to be represented in the            portfolio:            -   For each such other combined commodity, determine the                value of the SPAN requirement and the Available Net                Option Value for that other combined commodity, in the                performance bond currency of the original combined                commodity containing the position:                -   If the performance bond currency of this other                    combined commodity is the same as the performance                    bond currency of the combined commodity containing                    the positions, simply take the SPAN requirement and                    the Available Net Option Value for that other                    combined commodity.                -   But if these two currencies are not the same:                -   Multiply the SPAN requirement for the other combined                    commodity by the appropriate rate to convert it to                    the performance bond currency of the original                    combined commodity, and round this result to the                    normal precision for that original performance bond                    currency.                -   Multiply the Available Net Option Value for the                    other combined commodity by the same rate, and round                    this result to the normal precision for that                    original performance bond currency.            -   Take the sum of these equivalent values for SPAN                requirement, across all such other combined commodities.            -   Increment the SPAN requirement for the original combined                commodity containing the net position, by this sum.            -   Take the sum of the equivalent values for Available Net                Option Value, across all such other combined                commodities.            -   Increment the SPAN requirement for the original combined                commodity containing the net position, by this sum.        -   The result so far is the SPAN requirement and the Available            Net Option Value for the naked long (or naked short)            position for this directly calculated requirement level.        -   If any requirement levels are derived from this directly            calculated requirement level, apply the risk adjustment            factor(s) in turn to determine the derived SPAN risk            requirement and Available Net Option Value for the naked            long (or naked short) position for each such derived            requirement.

Aggregating SPAN requirements for Naked Positions with SPAN requirementsfor subaccounts: For each combined commodity represented in the omnibusaccount portfolio:

-   -   For each requirement level for which requirements have been        determined for this portfolio, whether directly or indirectly        calculated:        -   Take the sum of the SPAN risk requirements for this            requirement level across all subaccount portfolios in which            this combined commodity is represented. This yields the            total SPAN risk requirement for subaccounts for this            requirement level.        -   Similarly, take the sum of the Available Net Option Values            for this requirement level across all subaccount portfolios            in which this combined commodity is represented. This yields            the total Available Net Option Value for subaccounts for            this requirement level.        -   Take the sum of the total SPAN risk requirement for            subaccounts, and the total SPAN risk requirements for naked            positions, yielding the overall SPAN risk requirement for            the combined commodity and this requirement level.        -   Similarly, take the sum of the total Available Net Option            Value for subaccounts, and the total Available Net Option            Value for naked positions, yielding the overall Available            Net Option Value for the combined commodity and this            requirement level.

The SPAN Calculation for Gross-Margined Clearing-Level Accounts:Specification of gross clearing-level positions

As described above in the introductory section Portfolios to bemargined, when a clearing-level account is said to be gross-margined,this means the following.

First, positions are maintained on a gross basis. For any particularposition in the portfolio, a Total Long position and a Total Shortposition are defined.

Second, of the Total Long and Total Short position quantities, someportion is specified to be intercommodity spreadable and some portion issaid to be intracommodity spreadable. Positions that are neither internor intracommodity spreadable are naked.

So for each position in a gross-margined clearing-level portfolio, sixposition quantity values will be specified:

-   -   Total Long    -   Total Short    -   Intracommodity Spreadable Long    -   Intracommodity Spreadable Short    -   Intercommodity Spreadable Long    -   Intercommodity Spreadable Short    -   Naked Long    -   Naked Short

Note that we are following the same convention as with gross-marginedfirm-level accounts, where both long and short position quantities areexpressed as positive numbers.

At the CME, when clearing member firms report their positions for aprocessing cycle, they specify for each position the total long andshort quantities, the intracommodity spreadable long and shortquantities, and the intercommodity spreadable long and short quantities.

The naked long quantity is then determined by subtracting theintracommodity spreadable long quantity and the intercommodityspreadable long quantity from the total long quantity, and analogouslyfor the naked short quantity.

By definition, the total long quantity must always be the sum of theintracommodity spreadable long, the intercommodity spreadable long, andthe naked long. The total short must always be the sum of theintracommodity spreadable short, the intercommodity spreadable short,and the naked short.

Overall SPAN process for gross-margined clearing-level portfolios: Foreach position in the portfolio:

-   -   Determine the intracommodity spreadable net position quantity by        subtracting the intracommodity spreadable short quantity from        the intracommodity spreadable long quantity.    -   Determine the intercommodity spreadable net position quantity by        subtracting the intercommodity spreadable short quantity from        the intercommodity spreadable long quantity.    -   Process the portfolio of intercommodity spreadable net positions        through the SPAN algorithm as described above for net        portfolios. This yields, for each combined commodity in the        portfolio, for each directly and indirectly-calculated        requirement level for that combined commodity, the SPAN        requirement and the Available Net Option Value for the        intercommodity spreadable positions.    -   Process the portfolio of intracommodity spreadable net positions        through SPAN algorithm as described above for net portfolios,        but omit processing of all of the spread groups except the        intracommodity spread group. The result is, for each combined        commodity in the portfolio, for each directly and        indirectly-calculated requirement level for that combined        commodity, the SPAN requirement and the Available Net Option        Value for the intracommodity spreadable positions.    -   Process each naked long and naked short position through the        SPAN algorithm for naked positions, and aggregate the resulting        naked risk requirements and available net option values to the        combined commodity level, exactly as described above for omnibus        accounts. The result is, for each combined commodity in the        portfolio, for each directly and indirectly calculated        requirement level for that combined commodity, the SPAN        requirement and the Available Net Option Value for naked        positions.    -   For each combined commodity in the portfolio:        -   For each directly and indirectly calculated requirement            level for the combined commodity:            -   Take the sum of the SPAN risk requirement for                intercommodity spreadable positions, the SPAN risk                requirement for intracommodity spreadable positions, and                the SPAN risk requirement for naked positions. The                result is the total SPAN risk requirement for the                combined commodity for this requirement level.            -   Take the sum of the Available Net Option Value for                intercommodity spreadable positions, the Available Net                Option Value for intracommodity spreadable positions,                and the Available Net Option Value for naked positions.                The result is the total Available Net Option Value for                the combined commodity for this requirement level.

Aggregation of Values from Combined Commodities: Determining values touse for aggregation for each combined commodity

-   -   Determine the highest performance bond class for which        requirement have been calculated among all combined commodities        represented within the portfolio.    -   For each combined commodity in the portfolio:        -   For each such performance bond class for which requirements            have been calculated, beginning with the core class and            ascending in priority order to the highest class represented            in the portfolio:        -   If requirements were calculated for this class:            -   Use the calculated values for the following four values,                as the values to use for aggregation:                -   SPAN requirement—maintenance—specified class                -   SPAN requirement—initial—specified class                -   Available Net Option Value—maintenance—specified                    class                -   Available Net Option Value—initial—specified class        -   But if requirements were not calculated for this class for            this combined commodity:            -   Use the above four values for aggregation for the                immediately preceding class, as the values for                aggregation for this class.

Aggregation of currency-level requirements from combined commodities toreport groups, exchange complexes, and the overall portfolio level:

-   -   For each exchange complex represented in the portfolio:        -   For each combined commodity report group for this exchange            complex:            -   Determine the set of performance bond currencies                represented among the combined commodities for this                report group within this exchange complex.            -   For each such performance bond currency represented                within the group:        -   For each performance bond class for which requirements have            been calculated within the portfolio:            -   Take the sum of the values for aggregation, for this                class, for any combined commodity within the group with                this performance bond currency, of the following:                -   SPAN requirement—maintenance—specified class                -   SPAN requirement—initial—specified class                -   Available Net Option Value—maintenance—specified                    class                -   Available Net Option Value—initial—specified class            -   The result is the specified value, for the specified                class, for the specified performance bond currency, for                the specified report group with the specified exchange                complex.    -   For each exchange complex represented in the portfolio:        -   Determine the set of performance bond currencies represented            among the combined commodities within this exchange complex.        -   For each such performance bond currency represented within            the exchange complex:            -   For each performance bond class for which requirements                have been calculated within the portfolio:            -   Take the sum of the values for aggregation, for this                class, for any combined commodity within the exchange                complex with this performance bond currency, of the                following:                -   SPAN requirement—maintenance—specified class                -   SPAN requirement—initial—specified class                -   Available Net Option Value—maintenance—specified                    class                -   Available Net Option Value—initial—specified class            -   The result is the specified value, for the specified                class, for the specified performance bond currency, for                the specified exchange complex.    -   For the total portfolio:        -   Determine the set of performance bond currencies represented            among the combined commodities within the total portfolio.        -   For each such performance bond currency represented:            -   For each performance bond class for which requirements                have been calculated within the portfolio:            -   Take the sum of the values for aggregation, for this                class, for any combined commodity within the portfolio,                of the following:                -   SPAN requirement—maintenance—specified class                -   SPAN requirement—initial—specified class                -   Available Net Option Value—maintenance—specified                    class                -   Available Net Option Value—initial—specified class            -   The result is the specified value, for the specified                class, for the specified performance bond currency, for                the total portfolio.

Determining Portfolio-Currency Equivalent Requirement Values: For eachexchange complex within the portfolio:

-   -   For each report group within that exchange complex:        -   For each performance bond class for which requirements have            been calculated within the portfolio:            -   For each performance bond currency represented within                that report group:                -   Determine the portfolio-currency equivalents as                    specified below, of the following four values:                -   SPAN requirement—maintenance—specified class                -   SPAN requirement—initial—specified class                -   Available Net Option Value—maintenance—specified                    class                -   Available Net Option Value—initial—specified class                -   If the portfolio currency is equal to this                    performance bond currency, then the portfolio                    currency value is the specified value.                -   But if the portfolio currency is different from this                    performance bond currency, determine the portfolio                    currency equivalent value:                -   Multiply the value in the performance bond currency                    by the appropriate conversion rate. Then round to                    the normal precision for this portfolio currency.                -   Take the sum of the portfolio-currency equivalent                    value for the maintenance SPAN requirement for this                    class for the different performance bond currencies,                    yielding the total portfolio-currency equivalent                    value for the maintenance SPAN requirement for this                    class and this report group.                -   Take the sum of the portfolio-currency equivalent                    value for the initial SPAN requirement for this                    class for the different performance bond currencies,                    yielding the total portfolio-currency equivalent                    value for the initial SPAN requirement for this                    class and this report group.                -   Take the sum of the portfolio-currency equivalent                    value for the maintenance Available Net Option Value                    for this class for the different performance bond                    currencies, yielding the total portfolio-currency                    equivalent value for the maintenance Available Net                    Option Value for this class and this report group.                -   Take the sum of the portfolio-currency equivalent                    value for the initial Available Net Option Value for                    this class for the different performance bond                    currencies, yielding the total portfolio-currency                    equivalent value for the initial Available Net                    Option Value for this class and this report group.    -   For each exchange complex within the portfolio:        -   For each performance bond class for which requirements have            been calculated for this exchange complex within the            portfolio:            -   For each performance bond currency represented within                that exchange complex:            -   Determine the portfolio-currency equivalents as                specified below, of the following four values, exactly                as this was done above:                -   SPAN requirement—maintenance—specified class                -   SPAN requirement—initial—specified class                -   Available Net Option Value—maintenance—specified                    class                -   Available Net Option Value—initial—specified class            -   Take the sum of the portfolio-currency equivalent value                for the maintenance SPAN requirement for this class for                the different performance bond currencies, yielding the                total portfolio-currency equivalent value for the                maintenance SPAN requirement for this class and this                exchange complex.            -   Take the sum of the portfolio-currency equivalent value                for the initial SPAN requirement for this class for the                different performance bond currencies, yielding the                total portfolio-currency equivalent value for the                initial SPAN requirement for this class and this                exchange complex.            -   Take the sum of the portfolio-currency equivalent value                for the maintenance Available Net Option Value for this                class for the different performance bond currencies,                yielding the total portfolio-currency equivalent value                for the maintenance Available Net Option Value for this                class and this exchange complex.            -   Take the sum of the portfolio-currency equivalent value                for the initial Available Net Option Value for this                class for the different performance bond currencies,                yielding the total portfolio-currency equivalent value                for the initial Available Net Option Value for this                class and this exchange complex.    -   For the total portfolio:        -   For each performance bond class for which requirements have            been calculated within the portfolio:            -   For each performance bond currency represented within                the total portfolio:            -   Determine the portfolio-currency equivalents as                specified below, of the following four values, exactly                as this was done above:                -   SPAN requirement—maintenance—specified class                -   SPAN requirement—initial—specified class                -   Available Net Option Value—maintenance—specified                    class                -   Available Net Option Value—initial—specified class            -   Take the sum of the portfolio-currency equivalent value                for the maintenance SPAN requirement for this class for                the different performance bond currencies, yielding the                total portfolio-currency equivalent value for the                maintenance SPAN requirement for this class and the                total portfolio.            -   Take the sum of the portfolio-currency equivalent value                for the initial SPAN requirement for this class for the                different performance bond currencies, yielding the                total portfolio-currency equivalent value for the                initial SPAN requirement for this class and the total                portfolio.            -   Take the sum of the portfolio-currency equivalent value                for the maintenance Available Net Option Value for this                class for the different performance bond currencies,                yielding the total portfolio-currency equivalent value                for the maintenance Available Net Option Value for this                class and the total portfolio.            -   Take the sum of the portfolio-currency equivalent value                for the initial Available Net Option Value for this                class for the different performance bond currencies,                yielding the total portfolio-currency equivalent value                for the initial Available Net Option Value for this                class and the total portfolio.

Comparison of collateral to requirements and determination of whether anexcess or a deficiency exists: The SPAN algorithm determines the SPANrequirements and available net option value for the differentrequirement levels for each combined commodity within the portfolio, andaggregates of these values to the report group, exchange complex andtotal portfolio levels, both by performance bond currency representedand as equivalent values in the portfolio currency.

The valuation of collateral deposited to meet requirements, thecomparison of collateral to requirements and the determination of excessor deficit amounts is, strictly speaking, outside the scope of SPAN. Atthe clearing-level, and especially if requirements are calculated formore than one performance bond class and if various different types ofcollateral are accepted, this process can be complex.

For ordinary customer accounts at the firm-level, where only one classof performance bond requirement is calculated, the process is typicallymuch simpler, and is described herein.

-   -   Determine the overall value in the portfolio currency to be used        for margining (the “performance bond” value) of non-cash        collateral assets. This value is typically called the securities        on deposit.    -   Determine the net value in the portfolio currency of cash in the        account due to gains (or losses) on open positions in products        valued futures-style. This value is typically called the open        trade equity.    -   Determine the net value in the portfolio currency of all other        cash in the account. This value is typically called the ledger        balance.    -   Take the sum of the above three values, plus the available net        option value for the maintenance requirement for the core        performance bond class. This yields the funds available for        margin for the core maintenance requirement.    -   Take the sum of the above three values, plus the available net        option value for the initial requirement for the core class.        This yields the funds available for margin for the core initial        requirement.    -   Determine whether the portfolio is considered “new” or        “existing”:        -   If the portfolio contained no positions whatever at the            close of business for the preceding business day, then            portfolio is considered to be a new one.        -   Otherwise, the portfolio is considered to be a previously            existing one.    -   If the portfolio is considered “existing” and If the funds        available for margin for the maintenance requirement for the        core class, is greater than or equal to the core maintenance        SPAN requirement:        -   Then the maintenance requirement is deemed to be applicable.            The applicable SPAN risk requirement is the SPAN requirement            for maintenance for the core class, and the applicable funds            available for margin is equal to the funds available for            margin for maintenance for the core class.    -   But if the portfolio is considered “new” or if it is considered        existing, but the funds available for margin for the maintenance        requirement for the core class is less than the SPAN requirement        for maintenance for the core class:    -   Then the initial requirement is deemed to be applicable. The        applicable SPAN risk requirement is the SPAN requirement for        initial for the core class, and the applicable funds available        for margin is the funds available for margin for initial for the        core class.    -   Subtract the applicable SPAN requirement from the applicable        funds available for margin, yielding the excess (if this value        is positive) or deficit (if this value is negative) amount.

Note that in most cases for customer account types other thanspeculators, and in some cases for speculators, the initial requirementis equal to the maintenance requirement, and accordingly the initialfunds available for margin is equal to the maintenance funds availablefor margin. The logic described above simplifies substantially in thiscase.

Even in cases where initial requirements are different from maintenancerequirements, funds available for margin for initial is typically equalto funds available for margin for maintenance. These two values couldonly be different if combined commodities are represented within theportfolio for which the available net option value is capped at therisk.

FIG. 1 illustrates an exemplary risk management system 100 implementedto evaluate and quantify the risk, as well as determine a risk margin,for a portfolio of event driven instruments such as, for example, acredit default swap which may be triggered by an well-known ISDA-definedevents. Herein, the phrase “coupled with” is defined to mean directlyconnected to or indirectly connected through one or more intermediatecomponents. Such intermediate components may include both hardware andsoftware based components. Further, to clarify the use in the pendingclaims and to hereby provide notice to the public, the phrases “at leastone of <A>, <B>, . . . and <N>” or “at least one of <A>, <B>, . . . <N>,or combinations thereof” are defined by the applicants in the broadestsense, superceding any other implied definitions herebefore orhereinafter unless expressly asserted by the applicants to the contrary,to mean one or more elements selected from the group comprising A, B, .. . and N, that is to say, any combination of one or more of theelements A, B, . . . or N including any one element alone or incombination with one or more of the other elements which may alsoinclude, in combination, additional elements not listed.

The exemplary risk management system 100 includes a risk analysis engine102. The risk analysis engine 102 receives a portfolio 104 to beanalyzed and a set of parameters 108 that control the analysis. Theengine 102 then generates an assessment of the risk 110 associated withthe contracts and positions within the portfolio 104. In one embodiment,the engine 102 may also receive actual market data 106, real time orhistorical, to be factored into the risk analysis. In one embodiment,the risk analysis engine 102 is the SPAN® software published by theChicago Mercantile Exchange Inc., located in Chicago, Ill., describedabove. The portfolio 104, in many exemplary embodiments, is a data orrecord structure that contains and tracks the products, and positionsthereon, held by a given entity, such as a trader or clearing member,e.g., 3 month corn, 4 month Eurodollar, single name credit eventfutures, hurricane futures, credit event index futures, etc.; thecontracts, e.g., futures, options and credit-event futures; and thepositions, e.g., long or short for which the given entity has enteredinto but not closed out during a given trading period, i.e. the openpositions, for a given entity of interest. Credit events may beconsidered any situation or triggering event that affects a company orentity's credit or liquidity. Futures and options have been describedabove. Credit derivatives, such as credit-event futures may, forexample, be associated with companies, entities or positions in fiscaldistress such as a potential default or debt restructuring. A potentialcredit-event may be offset via the purchase of insurance or a guaranteeagainst the occurrence of the event. It will be understood that avariety of credit-events as defined by the International Swaps andDerivatives Association, Inc. (ISDA) may be occur based on variousoutside influences and their effects on the products or positions. Theentity for which the portfolio applies may be a trader, a brokeragehouse (all of the traders affiliated therewith), or a clearing member,etc.

The parameter set 108 used by the risk analysis engine 102, as describedabove, includes parameters which are determined by the entity, e.g. theexchange or the clearing member, performing the analysis to reflect therisk coverage desired in any particular market. These parameters 108 mayinclude, but are not limited to, any information, net notional, spread,term, etc. necessary to describe and identify a credit derivative suchas a credit default swap.

In operation, as described above, the portfolio 104 and parameter set108, and possibly the real-time and/or historical market data 106, areinput into the engine 102. The engine 102 processes the data andgenerates the assessment 110. The engine 102 may operate in batch toprocess multiple portfolios, using the same or different parameter sets108 and/or market data 106, or may process one portfolio 104 at a time.As was described above, the engine 102 may be operated by a clearinghouse of an exchange to assess actual required performance bonds, orchanges thereto. The engine 102 may also be operated by entities thatare subject to such performance bonds in order to anticipate therequirements of the clearing house. Further, engine 102, as describedbelow, provides accurate determinations as to the risk in the portfolio104 to ensure that the clearing house is adequately protected and thatthose subject to the bond requirements are not unduly burdened withunnecessary requirements.

In one embodiment, the engine 102 executes on a computer having aPentium®-class processor, or suitable equivalent, a hard disk drive, forexample a hard disk drive having a ten gigabyte capacity, a memory, forexample a memory having a one gigabyte capacity, and a suitable outputdevice such as flat panel LCD display. Further, the computer executes anappropriate operating system, such as Microsoft® Windows® XP, publishedby the Microsoft Corporation, located in Redmond, Wash. The computersystem 102 further may include a network interface and accompanyingsoftware for coupling the system with a network, the interface being ofa suitable type for the network, such as an Ethernet or optical basednetwork. The network may be a public or private network, such as theInternet, an intranet, a virtual private network, or other TCP/IP ornon-TCP/IP based network as is known. Further, secure protocols, such assHTTP or encryption, may be included to protect communications frombeing intercepted or modified and to generally authenticate users andensure secure operation. It will be appreciated that any suitablecomputer system having suitable processing, storage and communicationscapabilities may be used with the disclosed embodiments, such as amainframe computer, a mini-computer, a workstation, a personal computeror a personal digital assistant. It will be further appreciated that thedisclosed embodiments may be executed on a single computer system, orone or more component of the disclosed embodiments may be executed on acomputer system which is physically separate from one or more computersystem(s) executing the remaining of the components, and suitablyinterconnected, such as via a network.

While the disclosed embodiments relate to a computer software programwhich is stored in the memory of a computer and executed by theprocessor(s) of the computer to perform the disclosed functions, it willbe appreciated that one or more of the disclosed components may beimplemented in hardware or a combination of hardware and software, andis implementation dependent.

As shown in FIG. 2, the engine 102, in one embodiment, is configured toperform a multi-factor risk analysis or model related to one or morecredit default swap (CDS) within the portfolio 104. The portfolio 104,in this example, includes a plurality of CDS instruments individuallyindentified as 200 a to 200 n. The multi-factor risk analysis or modelmay be utilized to characterize and define forward-looking risk coveragefor price, liquidity, and “jump to default” risk. For example, themulti-factor analysis or model may be utilized to determine the size orvalue of a performance bond necessary to satisfy the margin requirementfor a portfolio of credit default swaps. The multi-factor risk model mayinclude and/or incorporate risk factors that are grouped and identifiedas macro risks describing the overall credit market risk; sector risksdescribing and addressing the risk within a specific segment (or sector)of the credit market and any additional or noteworthy risks or factors.

Macro risk includes and addresses systematic risk, curve risk and therisk associated with credit convergence and divergence. The engine 102may include a systematic risk module or processor 202 configured orprogrammed to execute or implement the systematic risk portion of themulti-factor risk analysis. Systematic risk gauges the market riskcontained within a portfolio by utilizing credit stress tests that move,shift or otherwise shock the current spread level of each individual CDSwithin a portfolio 104. In one embodiment, each CDS in the portfolio 104may be shocked up and down twelve percent (12%) in an attempt tocharacterize a historic one-day spread move or change with a ninety-ninepercent (99%) confidence interval. For example, if a CDS within theportfolio 104 currently trades at one-hundred (100) basis points, thespread would be stressed up (or increased) to one-hundred twelve (112)basis points and stressed down (or decreased) to eighty-eight (88) basispoints. The portfolio 104 may, in turn, be repriced utilizing thegathered shocked spread information to determine the maximum decrease ornegative change associated with the entire portfolio 104 due to an up ordown shock. The maximum decrease or negative change represents orcorresponds to the systematic risk margin.

Systematic risk, in another embodiment, captures the percentage changeof the spread associated with each CDS in the portfolio 104 in responseto an up or down shock. The shock applied to the spread curve may becalculated by maintaining or fixing the previous day's spread curve,while recalculating the previous five (5) years of historical data. Thesystematic risk and the associated systematic risk margin may includeall single-name references within the portfolio 104 as well as thesingle-name components of the indices. Exemplary indices may include anyCDS index such as, for example, CDX IG, HY, HVOL, XO, iTRAXX Europe,Financials and XO indices.

Curve risk attempts to address and quantify the possibility that the CDScurve may flatten or steepen. The engine 102 may include a curve riskmodule or processor 204 configured or programmed to execute or implementthe curve risk portion of the multi-factor risk analysis. Curve risk maybe characterized by moving, shifting or otherwise shocking the spreadsbased on the tenor associated with each CDS contained within theportfolio 104. For example, a CDS with a spread having a shorter tenor(less remaining term) may be shifted or shocked higher while a CDS witha spread a having a longer tenor (more remaining terms) may be shiftedor shocked lower. Alternatively, the shifts may be reversed so that aCDS having a spread with a longer tenor may be shocked higher and viceversa. In one exemplary embodiment a first curve scenario may beutilized such that the 1 yr and 3 yr spreads are shocked up while the 7yr and 10 yr spreads shocked down, and a second curve scenario may beutilized such that the 1 yr and 3 yr spreads are shocked down while the7 yr and 10 yr spreads shocked up. Both scenarios are executed for eachCDS position in the portfolio 104. The magnitude is calculated based ontaking the relative moves of the 1 yr, 3 yr, 7 yr and 10 yr spreads to 5yr for all names and then building four (4) distributions (one for eachof the 1 yr, 3 yr, 7 yr and 10 yr relative to the 5 yr) and then taking99% confidence level.

In operation, once the shape of the curve has been alternativelyflattened or steepened, each CDS in the portfolio 104 may be repricedutilizing the gathered spread information to determine the maximumdecrease or negative change associated with the entire portfolio 104 dueto an up or down shock. The maximum decrease or negative changerepresents or corresponds to the curve risk margin. The curve risk andthe associated curve risk margin may include all single-name referenceswithin the portfolio 104 as well as the single-name components of theindices. Moreover, the change or adjustment to the shape of the spreadcurve may be adjusted or calibrated to account for or reflect thelargest one-day historical move with a ninety-nice percent (99%)confidence interval.

Credit spread convergence and divergence captures and characterizes theoverall risk of the spreads associated with each high-yield CDS in theportfolio relative to the spreads associated with an investment-gradeCDS. This scenario corresponds to that a synthetic portfolio of allinvestment grade names and a synthetic portfolio of all high yieldnames. Convergence is said to occur when the investment grade spreads goup and the high yield spreads go down. Divergence is the inverse. Theengine 102 may include a convergence and divergence risk module orprocessor 206 configured or programmed to execute or implement theconvergence and divergence risk portion of the multi-factor riskanalysis. Credit spread convergence and divergence implemented in thismanner, addresses the risk of selling protecting in a high-yield CDS andbuying protection in a corresponding investment grade CDS. For example,a CDS having a spread of four hundred (400) basis points or more may bedefined as a high-yield CDS and shifted or shocked downward by sixpercent (6%) while a similar investment grade CDS may be shifted orshocked upward by six percent (6%). Alternatively, the relative shiftsbetween the high-yield CDS and the investment grade CDS may be reversedand/or the absolute magnitude of the shift may be altered. The largestnegative change in the value of the portfolio 104 indicates the riskmargin associated with the characterized convergence and/or divergence.The curve risk and the associated curve risk margin may include allsingle-name references within the portfolio 104 as well as thesingle-name components of the indices. Moreover, the change oradjustment to the shape of the spread curve may be adjusted orcalibrated to account for or reflect the largest one-day historical movewith a ninety-nice percent (99%) confidence interval.

The sector risks address and quantify the risk associated with aspecific business, manufacturing or other area or group. The engine 102may include a sector risk module or processor 208 configured orprogrammed to execute or implement the sector risk portion of themulti-factor risk analysis. Each CDS within the portfolio 104 will beassigned to one of ten sectors. Each of the ten sectors will beindividually shocked or stressed to illustrate hypothetical spread movesup and down for each CDS assigned to a given sector. The sectoridentified as having the highest or greatest sector risk will, in turn,be utilized as the sector margin for the entire portfolio. The tensectors are identified as: (i) basic materials; (ii) consumernon-cyclical; (iii) consumer cyclical; (iv) financials; (v) health care;(vi) industrials; (vii) oil & gas; (viii) technology; (ix)telecommunications; and (x) utilities.

In operation, each CDS within one of the identified sectors (i) to (x)is shocked or otherwise shifted up or down by nine percent (9%) tocharacterize the largest one-day shift in any given sector with aninety-nine percent (99%) confidence interval. The sector determined tohave the largest negative change (i.e., maximum loss) is the worstperforming sector and provided the basis for the sector risk margin. Itwill be understood that the amount by which the sectors are shocked maybe adjusted or calibrated to reflected any desirable confidence intervalor any other historical trend or data.

Idiosyncratic risk may be utilized to estimate the effects of an extremespread move or shift for the largest (greatest volume or number) singlename or group of CDS within the portfolio 104. The engine 102 mayinclude an idiosyncratic risk module or processor 210 configured orprogrammed to execute or implement the idiosyncratic risk portion of themulti-factor risk analysis. For example, as shown in Table 1, each CDSwithin the portfolio 104 may be grouped or assigned to a bucketaccording to a spread.

TABLE 1 Idiosyncratic risk factors and bucket criteria. IdiosyncraticFactor to cover a five (5) day Bucket Number Spread Bucket move (%) 1 0-50 1 2 51-75 1 3  76-100 2 4 101-150 3 5 151-200 4 6 201-300 5 7301-400 5 8 401-500 7.5 9 501-750 10 10  751-1000 12.5 11 1001-1500 1512 1501-2000 17.5 13 >2000 20Based on the bucket number and the associated spread bucket, anidiosyncratic spread factor may be defined to represent the greatestfive (5) day historical spread move or shift with an ninety-nine percent(99%) confidence interval. Idiosyncratic risk captures specific entitylevel risks of CDS spreads moving by large amounts that may not bereflected and/or accounted for by the macro risk or sector risk and maybe calculated as the net notional of the specific entity multiplied bythe idiosyncratic factor defined in Table 1. The idiosyncratic marginequals the two most negative calculated idiosyncratic risks.

Liquidity risk represents a risk associated with a portfolio 104including a large number of illiquid CDS such as large, single namepositions, which may be determined, based on, for example, open interestand volume data. The engine 102 may include a liquidity risk module orprocessor 212 configured or programmed to execute or implement theliquidity risk portion of the multi-factor risk analysis. Depending onthe liquidity risk, the required margin requirement may be increasedbased on a net notional basis by name. For example, as shown in Table 2,each large, single name CDS within the portfolio 104 may be grouped orassigned to a bucket according to a spread and minimum threshold value.

TABLE 2 Liquidity risk factors and bucket criteria. Minimum LiquidityThreshold Factor Bucket Number Spread Bucket ($ Millions) (Percent) 1 0-50 250 0.125 2 51-75 200 0.150 3  76-100 200 0.200 4 101-150 1500.225 5 151-200 150 0.300 6 201-300 125 0.375 7 301-400 100 0.400 8401-500 100 0.500 9 501-750 75 0.5625 10  751-1000 50 1.000 11 1001-150050 1.000 12 1501-2000 35 1.250 13 >2000 25 1.500Based on the bucket number and the associated spread bucket and minimumthreshold, a liquidity spread factor determined to reflect the riskassociated with a high concentration of illiquid CDS within theportfolio 104. The liquidity spread factor may be revised to reflectincreased transparency provided by the Depository Trust & ClearingCorporation (DTCC). The liquidity spread factor may be initiallydetermined based on trader feedback and/or from DTCC and CME CDSexchange data such as open interest and volume.

In operation, an exemplary CDS that trades as 125 basis points and has anet notional position of $550M corresponds to a liquidity risk factor of0.225%. The liquidity margin may be determined as the excess orremainder of the net notional amount above the minimum thresholdmultiplied by liquidity risk factor. Referring to the previous example,the liquidity margin for a given illiquid CDS corresponding to bucket orgroup 5 equals $400M ($550M-$150M) multiplied by 0.00225 and equals$900K. The overall liquidity margin is the sum of all the individualliquidity margins associated with each of the identified illiquid CDSpositions within the portfolio 104.

Basis risk represents the risk associated with the richening orcheapening of a CDS index against the theoretical prices based on theunderlying components (“Fair Value”). The engine 102 may include a basisrisk module or processor 214 configured or programmed to execute orimplement the basis risk portion of the multi-factor risk analysis. Thebasis charge for each CDS index in the portfolio 104 equals the netnotional of the index multiplied by a basis risk factor associated withthe index. The basis factor may be 0.2% for an investment grade indexand 0.5% for a high yield index. The basis factor for each type of indexmay be calculated to reflect the largest one-day spread change with aninety-five percent (95%) confidence interval. The overall basis marginis the sum of all the individual basis charges associated with each CDSindex within the portfolio 104.

The engine 102 further includes a margin adjustment processor 216. Theengine 102 receives input or information representing CDS instruments200 a, 200 b, 200 c, 200 d, 200 e, . . . 200 n, contained within theportfolio 104. The received information may be communicated to themodules or subroutines 202 to 214 in a series or parallel manner. Eachof the modules 202 to 214, in turn, may determine and communicate amodule margin requirement. The margin adjustment processor 208 mayreceive the module margin requirement determined by the modules 202 to214. The received module margin requirements can be combined toaccurately compute the requisite performance bond representative of therisk 110 associated with the CDS portfolio 104.

In one exemplary embodiment, a computer or computer network may beconfigured to conduct a multi-factor spread risk analysis process on aportfolio. For example, the computer may include a processor and amemory communicatively coupled to the memory. The memory may be amagnetic storage device, an optical storage device or any other type ofinformation storage mechanism. Alternatively, the memory or logic may bean array of logic switches or gates that mechanically operate in amanner equivalent to stored program logic. Thus, the logic may beconfigured to communicatively cooperate with the processor to conduct adiversification risk analysis.

In a physical and operational sense, the processor may provide inputs tothe physical logic and receive outputs from the logic circuits. Theinputs may include information related to the overall CDS portfolio 104and the included CDS instruments 200 a:200 n within that portfolio 104.The physical or program logic may, in turn, perform or execute amulti-factor risk analysis based on the provided inputs and information.The results of the implemented or executed multi-factor risk analysismay, in turn, determine the size of a performance bond and/or marginrequired to cover the risk associated with the CDS instruments withinthe portfolio 104.

It is therefore intended that the foregoing detailed description beregarded as illustrative rather than limiting, and that it be understoodthat it is the following claims, including all equivalents, that areintended to define the spirit and scope of this invention.

1. A method for determining a margin requirement associated with aplurality of financial instruments within a portfolio, the methodcomprising: receiving a plurality of data associated with the pluralityof financial instruments within the portfolio; determining, using aprocessor, a systematic risk margin based on at least a portion of thereceived plurality of data; determining, using the processor, a curverisk margin based on at least a second portion of the received pluralityof data; determining, using the processor, a convergence and divergencerisk margin based on at least a third portion of the received pluralityof data; determining, using the processor, a sector risk margin based onat least a fourth portion of the received plurality of data;determining, using the processor, an idiosyncratic risk margin based onat least a fifth portion of the received plurality of data; determining,using the processor, a liquidity risk margin based on at least a sixthportion of the received plurality of data; determining, using theprocessor, a basis risk margin based on at least a seventh portion ofthe received plurality of data; and calculating, using the processor, amulti-factor risk margin based on one more of the determined riskfactors.
 2. The method of claim 1, wherein at least one of the pluralityof financial product comprises a credit derivative.
 3. The method ofclaim 2, wherein the credit derivative comprises a credit default swap.4. The method of claim 1, wherein calculating a multi-factor risk marginincluding summing a systematic risk margin, a curve risk margin, aconvergence and divergence risk margin, a sector risk margin, anidiosyncratic risk margin, a liquidity risk margin, and a basis riskmargin.
 5. A method for determining a margin requirement associated witha plurality of financial instruments within a portfolio, the methodcomprising: receiving a plurality of data associated with the pluralityof financial instruments within the portfolio; determining, using aprocessor, a systematic risk margin based on at least a portion of thereceived plurality of data; determining, using the processor, a sectorrisk margin based on at least a fourth portion of the received pluralityof data; and calculating, using the processor, a multi-factor riskmargin based on one more of the determined risk factors.
 6. The methodof claim 5 further comprising: determining a curve risk margin based onat least a second portion of the received plurality of data.
 7. Themethod of claim 5 further comprising: determining a convergence anddivergence risk margin based on at least a third portion of the receivedplurality of data.
 8. The method of claim 5 further comprising:determining an idiosyncratic risk margin based on at least a fifthportion of the received plurality of data.
 9. The method of claim 5further comprising: determining a liquidity risk margin based on atleast a sixth portion of the received plurality of data; and determininga basis risk margin based on at least a seventh portion of the receivedplurality of data.
 10. The method of claim 5, wherein at least one ofthe plurality of financial product comprises a credit derivative. 11.The method of claim 10, wherein the credit derivative comprises a creditdefault swap.
 12. The method of claim 5, wherein calculating amulti-factor risk margin including summing a systematic risk margin, acurve risk margin, a convergence and divergence risk margin, a sectorrisk margin, an idiosyncratic risk margin, a liquidity risk margin, anda basis risk margin.
 13. A system for managing risk associated with aportfolio of financial instruments traded on an exchange, the systemcomprising: a processor; a memory in communication with the processor,the memory configured to store a program logic, wherein the programlogic is executable on the processor and is configured to: receive aplurality of data associated with the plurality of financial instrumentswithin the portfolio; determine a systematic risk margin based on atleast a portion of the received plurality of data; determine a sectorrisk margin based on at least a fourth portion of the received pluralityof data; calculate a multi-factor risk margin based on one more of thedetermined risk factors; and send data indicative of the multi-factorrisk margin to an output device.
 14. The system of claim 13, whereinprogram logic is further configured to: determine a curve risk marginbased on at least a second portion of the received plurality of data.15. The system of claim 13, wherein program logic is further configuredto: determine a convergence and divergence risk margin based on at leasta third portion of the received plurality of data.
 16. The system ofclaim 13, wherein program logic is further configured to: determine anidiosyncratic risk margin based on at least a fifth portion of thereceived plurality of data.
 17. The system of claim 13, wherein programlogic is further configured to: determine a liquidity risk margin basedon at least a sixth portion of the received plurality of data; anddetermine a basis risk margin based on at least a seventh portion of thereceived plurality of data.
 18. The system of claim 13, wherein at leastone of the plurality of financial product comprises a credit derivative.19. The system of claim 18, wherein the credit derivative comprises acredit default swap.
 20. The system of claim 13, wherein calculating amulti-factor risk margin including summing a systematic risk margin, acurve risk margin, a convergence and divergence risk margin, a sectorrisk margin, an idiosyncratic risk margin, a liquidity risk margin, anda basis risk margin.